De verpleegkundige zei dat ik mijn arm rustig moest houden, zodat de wond sneller beter wordt.

Yes. De verpleegkundige means the nurse, and it is normally a gender-neutral word.

Dutch also has older/more specific words like verpleger and verpleegster, but verpleegkundige is the standard neutral term you will often see and hear.

The article is de because verpleegkundige is a de-word.

Here dat means that.

The phrase zei dat... means said that... and introduces a subordinate clause:

• De verpleegkundige zei = The nurse said
• dat ik mijn arm rustig moest houden = that I had to keep my arm still

In Dutch, when dat introduces a clause, the verb usually moves toward the end of that clause. That is why the word order looks different from English.

Because this is a subordinate clause introduced by dat.

In a main clause, Dutch usually has the finite verb in second position. But in a subordinate clause, the verbs move to the end.

So:

• main clause style: Ik moest mijn arm rustig houden
• subordinate clause style: ... dat ik mijn arm rustig moest houden

Inside that clause:

• ik = subject
• mijn arm = object
• rustig = predicative adjective, describing how the arm should be kept
• moest houden = verb cluster at the end

That final verb placement is one of the most important Dutch word-order patterns to get used to.

Because moeten is a modal verb, and modal verbs usually combine with another verb in the infinitive.

So:

• moest = had to
• houden = keep

Together, moest houden means had to keep.

Compare:

• Ik moest gaan. = I had to go.
• Ik moest wachten. = I had to wait.
• Ik moest mijn arm rustig houden. = I had to keep my arm still.

You cannot usually stop at moest if you still need to say what the person had to do.

Yes, rustig often means calm, quiet, or still. But in this sentence, mijn arm rustig houden means to keep my arm still or not move it much.

So the meaning is not that the arm should be emotionally calm, of course. It is about avoiding movement.

This is very natural Dutch. With body parts, rustig houden often means:

• rest it
• keep it still
• do not strain it

Dutch often uses a possessive with body parts, especially when it is important to make clear whose body part is meant.

So mijn arm = my arm is very normal here.

Sometimes Dutch can also use de with body parts in certain constructions, especially when the owner is already obvious from the sentence, but mijn arm is completely natural and straightforward.

Zodat means so that.

It introduces a clause that gives a purpose or intended result:

• ... zodat de wond sneller beter wordt
• ... so that the wound gets better faster

In other words, the nurse told the speaker to keep the arm still with the goal that the wound would heal more quickly.

A useful contrast:

• want = because
• zodat = so that / in order that

So zodat is not giving the reason for the instruction; it is giving the desired result of following the instruction.

Because zodat is used when the result clause has its own subject and finite verb.

Here the subject of the result clause is de wond:

• de wond ... wordt

That is why zodat fits well.

Om ... te is more common when you have the same subject and an infinitive construction. For example:

• Ik oefen elke dag om beter te worden.
• I practise every day to get better.

But in your sentence, the thing that gets better is the wound, so a full clause with zodat is the natural choice.

That is because beter worden is a very common Dutch expression meaning to get better or to improve.

So:

• beter worden = get better
• sneller beter worden = get better faster

Here sneller modifies the whole process of recovery.

It may feel unusual if you translate word by word, but it is idiomatic Dutch.

A near-synonym would be:

• zodat de wond sneller geneest
• so that the wound heals faster

Both are natural. Beter worden is a little broader and more everyday; genezen is more specifically to heal.

This is a very common thing learners notice.

Dutch often uses the present tense in a purpose/result clause like this when the result is still seen as generally valid or expected to happen after the moment of speaking.

So:

• De verpleegkundige zei...
• the speaking happened in the past

but:

• zodat de wond sneller beter wordt
• the healing is the intended result, and that result is still relevant afterward

In natural English, you might sometimes expect would get better faster, but Dutch does not always shift the tense in the same way English does.

So this sentence is normal Dutch.

You may also come across past-tense versions in some contexts, but wordt sounds very natural here because the purpose is still current from the speaker’s point of view.