Krdytkyu

If your witch is going to make her living calling rain and healing, she needs to charge enough to live on; otherwise, "witch" is a sideline or hobby and she'll have to make her living doing something else (innkeeper, brewer, seamstress, potter, etc.).

That means she needs to earn (roughly) at least what a farmer, shopkeeper, or blacksmith does. Once you know that, and how many times she can use her magic in a day, you can calculate what she needs to charge. Then, of course, you need to know if her neighbors can afford (and are willing) to pay that for her services. I'd expect healing to pay better than calling rain, since nature produces enough rain in most places, most of the time.

Also, as noted in comments, there's the question of operating costs. Just as the blacksmith must price in the iron or steel that goes into the horseshoes, nails, and other goods he makes, or the farmer must price in feed for the animals that pull his plow, if the witch's materials are more expensive, her services also must be, or she must accept a lower margin.

Political power, in its basic form, comes from loyalty. Heal a close family member of a powerful person, and you're likely to gain loyalty from that person or others in their household. Put rain in one county and keep it from another, and the county that has what they want (whether it's the end of a drought, or protection from flooding) and knows who gave it to them will tend to appreciate it. In the end, a witch would gain political power the same way anyone else does -- by being popular and doing favors for those who can repay them in a political way.

Prices are set by meeting request and offer.

Everyone can charge as much as others are willing to pay for their product/service.

I can charge as much as Cristiano Ronaldo does for kicking a ball while wearing shorts, but I am sure I would find nobody willing to pay that amount, while Ronaldo does.

Regarding the political influence, a medieval kingdom is highly sensitive to weather: drought or flooding by rain can easily knock a kingdom down. The witch just needs to show she can control her power, and any one would understand she cannot be left disgruntled.

It depends on the service, costs for the witch and social standing of the witch.

Say that creating rain takes three days of doing a variety of chants. There's no material cost so the only factors are how difficult it is to the chants and the time it takes to do them. The time could ofcourse increase if the chant affects only a limited area.

Now she needs to heal which requires some ingredients that are expendes during the magic. Expensive ingredients? Expensive spell. You could allow people to bring the ingredients and reduce the cost in some cases.

Social standing is also important. Imagine if the witch healed someone's pigs and got paid. Later the pigs get sick again, is the witch making the pigs sick on purpose to get more work and pay? You dont know, and a witch with a low social standing will sooner be getting less pay (its your fault so you dont get much of my money), or she get's ousted or killed for sickness, disasters and problems that could be attributed to her magic. Whatever she does, she must always be clear to her customers and her neighbours about what she can do for them and when/how she punishes people using magic.

Whatever the Lord allows her to charge.

If magic is rare and effective, chances are your witch already works for the lord and is paid very well. She generally wouldn't charge for a particular service but would receive a periodical allowance. She offers her services only to the people the Lord allows.

She might live in a lands lent by the lord, or even offered, in which case the witch is herself a noble. She commands everyone in her lands.
This is what medieval means.

Can she have a shop in the city and act as a regular shop owner? Maybe if she only does practical tricks, divination etc. spells that can't be seen as dangerous and doesn't step on other guild's feet (maybe you have physicians, apothecaries, or even entertainers that don't appreciate what they might see as unfair competition). She might need to negotiate what spells she can perform and charge for.
Or, she could have an arrangement with the mayor that gives her a certain amount of authority to use her power.

If she lives isolated (like in typical cabin hidden in the woods) she can charge whatever she wants as far as she can defend herself. One important thing is if magic allows her to survive (can she grow vegetables or obtain water by magic?). In that case she can charge whatever she wants, probably would try to base the price on the client's wealth.

how would she gain political power from it?

Tomás has already laid the basis for my answer.

Work your way up to the top

For someone who is not noble by birth, you have to work your way up the social ladder from the bottom. News of a valuable resource travels upwards in a medieval society. Provided witches are not condemned for their abilities, you first ingratiate yourself with the local mayor, doing favours and giving advice and not asking too much in return except for exemptions from local taxes and so on. Soon the local lord will hear of this and will appropriate your services from the mayor. Of course he will offer you blandishments like good food and a fine room to live in to persuade you to move.

Sooner or later the news of your value will percolate up to the queen. She will order whoever you are with to release yo to her service. It is now your job to become her most trusted personal adviser and licensed purveyor of spells.

Despite your lack of noble birth you are immensely powerful. The queen does what you suggest but of course she takes the credit if it goes well. Your magic makes sure it does go well. Because of the combination of your magical powers coupled with the Queen's protection, all the other courtiers are respectful towards you and eager to do little favours in return for your help with a head cold or case of indigestion.

Medieval times weren't great at supply & demand vs working at swordpoint.

These are all fairly relevant to the question:

How easily can her services be forced?

What sort of kingdom is she in, socially?

Does it have any kind of legal system or concept of rights of peasants?

Can the king throw her in a cell and force her to heal his best soldiers under threat of death for her and everyone she cares about, North Korea style?

If she has no powerful friends, that could be her fate: to find herself locked up and used as a resource of the state.

On the other hand, if she either has the favor of some nobles such that she can't just disappear, or if the kingdom has some kind of trader class and a legal system that has some kind of respect for individual rights of commoners... then she could become fantastically wealthy.

Rain.... rain is worth something, particularly if she can call enough rain for thousands of square miles, but it's nothing compared to healing if she can heal serious things.

How many nobles are there within reasonable travel distance from her? Thousands? In medieval times commoners saw child mortality rates of 30-50%. Nobles weren't much better off.

A few thousand nobles will include hundreds of people with dying kids, wives facing non-trivial risk of death during childbirth, lots of people occasionally facing possible death from what would now be treatable infections and lots of elderly counts and barons facing all the horrors of old age.

If her magic can clear a chest infection from a dying child or save a prince dying from sepsis from an infected wound.... saying that she would be highly in demand puts it lightly. She would be worth her weight in gold, literally.

If she found herself attached to a noble household we'd expect to see the rich and powerful making journeys to her with sick family members, and access to her would be used as a political bargaining coin.

If magic users were more common then you'd expect it to be routine for any noble house to have a mage associated with them.

The more common you make them the lower down the social hierarchy access to mages goes.