La médica me dice que no me rasque la picadura para que no empeore.

Because médica is the feminine form of médico.

• el médico = the male doctor / the doctor
• la médica = the female doctor

In modern Spanish, especially in Spain, la médica is a normal and standard way to refer to a female doctor. You may also hear la doctora, but that can sometimes sound more like doctor as a title, while médica clearly means female physician.

They do two different jobs.

• me dice = tells me
• no me rasque = that I not scratch myself / the bite on me

So:

• the first me goes with decir and shows who receives the information
• the second me goes with rascarse-type usage and shows who is affected by the scratching

They are not redundant; each one belongs to a different part of the sentence.

Because this is the present subjunctive, and the subject is yo.

The structure decir que + subjunctive is often used when reporting an order, instruction, or advice:

• La médica me dice que no me rasque... = The doctor tells me not to scratch...

Here, the doctor is giving advice or an instruction, so Spanish uses the subjunctive in the subordinate clause.

Why rasque specifically?

• infinitive: rascar
• present subjunctive, yo form: rasque

There is also a spelling change:

• c → qu before e

This keeps the hard k sound:

• rascar
• rasque

Because this sentence is reported speech, not a direct quote.

If the doctor were speaking directly to you, she might say:

• No te rasques la picadura. = Don’t scratch the bite.

But when you report that idea from your own point of view, Spanish changes the structure:

• La médica me dice que no me rasque la picadura.

So the person changes:

• direct speech: te rasques / te rasques-type idea
• reported speech: me rasque

In other words, it means:

• The doctor tells me not to scratch the bite.

Because Spanish very often uses the definite article instead of a possessive when it is already clear whose body part, injury, or affected area is meant.

Here, me already tells us that the bite is on me / affecting me, so la picadura is enough.

This is similar to patterns like:

• Me lavo las manos. = I wash my hands.
  • literally: I wash myself the hands

So:

• no me rasque la picadura = not scratch the bite = more naturally, not scratch my bite

Using mi picadura is possible, but it would usually sound more emphatic or contrastive, not the most neutral choice here.

Because para que is used to express purpose when there is a conjugated verb after it.

Here:

• para que = so that
• no empeore = it doesn’t get worse

So the phrase means:

• so that it doesn’t get worse

Also, after para que, Spanish normally uses the subjunctive, which is why we get empeore rather than empeora.

The subject is la picadura.

So:

• la picadura = the bite
• empeore = gets worse

That part of the sentence means:

• so that the bite doesn’t get worse

The verb is singular because la picadura is singular.

Not with the same meaning as naturally.

• para que no empeore = so that it doesn’t get worse
• para no empeorar would mean something more like in order not to get worse

The infinitive structure para + infinitive is usually used when the subject is the same as in the main clause. But here the thing that gets worse is the bite, not the doctor and not really I as the grammatical subject of the earlier verb.

So para que no empeore is the natural choice.

It can mean bite or sting, depending on context.

For example:

• mosquito bite
• insect bite
• bee/wasp sting

Spanish often uses picadura for both, because the exact type is usually understood from the situation. So if the sentence just says la picadura, it could refer to either a bite or a sting.

A useful way to see it is:

• La médica = subject
• me dice = main verb + indirect object
• que no me rasque la picadura = reported advice/instruction
• para que no empeore = purpose clause

So the pattern is roughly:

• [Person] + me dice que + subjunctive + para que + subjunctive

This is a very common Spanish pattern for reporting advice, instructions, or warnings.