Legen sier at jeg kan ta smertestillende hvis det gjør vondt i håndleddet.

Because legen is the definite singular form of lege.

• en lege = a doctor
• legen = the doctor

So Legen sier ... means The doctor says ...

Norwegian usually attaches the definite article to the end of the noun instead of using a separate word like the.

At means that.

So:

• Legen sier at ... = The doctor says that ...

In English, that is often optional:

• The doctor says I can take ...
• The doctor says that I can take ...

In Norwegian, at is very common after verbs like si (say), vite (know), tro (think/believe), and mene (mean/think).

Because kan is a modal verb, and modal verbs are followed by the infinitive without å.

So:

• jeg kan ta = I can take
• not jeg kan tar
• not jeg kan å ta

This is the same pattern as:

• jeg må gå = I must go
• jeg vil spise = I want to eat
• jeg skal jobbe = I will/am going to work

After a modal verb, the next verb stays in the infinitive form.

Smertestillende means painkillers or pain-relieving medicine.

It is built from:

• smerte = pain
• stillende = relieving / calming / stopping

Literally, it is something like pain-relieving.

In this sentence, it is being used as a noun, referring to pain medicine in a general sense. Norwegian often uses it this way without an article:

• ta smertestillende = take painkillers / take pain medicine

If you wanted to be more specific, you could say something like:

• ta en smertestillende tablett = take a painkiller tablet

Because here it is used in a general, non-count sense, like pain medication.

So:

• ta smertestillende = take painkillers / take pain medicine in general

This is very natural in Norwegian. English also sometimes does something similar with mass nouns:

• take medicine
• take medication

If you wanted to emphasize one pill or tablet, Norwegian would usually make that more explicit.

Hvis means if and introduces a condition.

So:

• hvis det gjør vondt = if it hurts

This suggests the pain may or may not happen.

A learner often wonders about hvis vs når:

• hvis = if
• når = when

Use hvis when something is conditional or uncertain. Use når when it is expected or treated as something that will happen.

So here, hvis makes sense because the doctor is saying painkillers are okay in case the wrist starts hurting.

Det gjør vondt is the standard Norwegian way to say it hurts.

Literally, it is something like:

• det = it
• gjør = does / makes
• vondt = painful / sore / badly

So the literal structure is not exactly the same as English, but the meaning is simply it hurts.

This is an idiomatic expression, and it is extremely common. You should learn it as a fixed pattern:

• Det gjør vondt = It hurts
• Det gjør vondt i ryggen = My back hurts / It hurts in my back
• Det gjorde vondt = It hurt

Because vondt is the form used in this expression.

The adjective is:

• vond in some forms
• vondt in the neuter/predicate form

In expressions like:

• Det er vondt
• Det gjør vondt

Norwegian uses vondt, not vond.

So this is another pattern worth memorizing as a chunk:

• gjøre vondt = to hurt

Håndledd means wrist, and håndleddet means the wrist.

It is a neuter noun:

• et håndledd = a wrist
• håndleddet = the wrist

So:

• i håndleddet = in the wrist

The preposition i is used here to indicate where the pain is located.

A very important point for English speakers: with body parts, Norwegian often uses the definite form where English might use my, your, etc., if it is already clear whose body part is meant.

So i håndleddet naturally means in the wrist, and in context we understand it means in my wrist because the subject is jeg.

Because Norwegian often avoids possessives with body parts when the owner is obvious from the context.

So instead of saying:

• i mitt håndledd = in my wrist

Norwegian very often prefers:

• i håndleddet = in the wrist

This is especially common when talking about pain, injuries, physical sensations, clothing, and body parts.

English uses possessives more often:

• my wrist hurts

Norwegian often uses the definite noun instead:

• det gjør vondt i håndleddet

Norwegian does have verb-second word order in main clauses, but not in the same way inside subordinate clauses.

Main clause:

• Jeg kan ta smertestillende.
• subject jeg
  • verb kan

Subordinate clauses introduced by words like at and hvis:

• at jeg kan ta smertestillende
• hvis det gjør vondt i håndleddet

So after at and hvis, the clause keeps a more regular subject + verb order.

This is an important distinction:

• Main clause: verb-second
• Subordinate clause: no normal V2 inversion

That is why the sentence looks the way it does.

Yes, that would also be understandable and natural.

• hvis det gjør vondt i håndleddet = if it hurts in the wrist
• hvis håndleddet gjør vondt = if the wrist hurts

The version in your sentence is very common because Norwegian often uses the impersonal pattern det gjør vondt i ... when talking about pain in a body part.

So the original wording is especially useful to learn as a standard expression.