jinryoga kkeutnago naseo yakgugeseo yageul sayo.

Not exactly.

• 진료 = medical examination / consultation / seeing a doctor
• 치료 = treatment / medical treatment

So in this sentence, 진료가 끝나고 나서 usually means after the doctor’s appointment/exam is over, not necessarily after all treatment is finished.

Because 끝나다 is an intransitive verb, meaning to end / be finished.

That means the thing that ends is marked as the subject, so you use 가/이:

• 진료가 끝나다 = the appointment ends

If you wanted a transitive version, Korean has 끝내다, meaning to finish something:

• 진료를 끝내다 = to finish the appointment
  but this sounds more like someone actively finishes it

In your sentence, the natural idea is simply the appointment ends, so 진료가 is correct.

-고 나서 means after doing..., with a clear sense that the first action happens first, and then the next action happens afterward.

So:

• 끝나고 나서 = after it ends
• 진료가 끝나고 나서 약국에서 약을 사요 = After the appointment ends, I buy medicine at the pharmacy

This pattern is very common for sequencing actions.

It can look redundant at first, but -고 나서 is a fixed and very common grammar pattern.

Compare:

• 끝나고 = it ends, and...
• 끝나고 나서 = after it ends

So -고 나서 is stronger and clearer about the time order. It emphasizes that the second action happens after the first one is completed.

In everyday Korean, this is completely natural.

Yes, you could, but the nuance is a little different.

• 끝나고 나서 focuses on sequence: first it ends, then I buy medicine
• 끝나서 can mean because it ended or simply connect the actions more loosely

So if your goal is specifically after the appointment, then 끝나고 나서 is often the clearer choice.

Because 에서 marks the place where an action happens.

• 약국에서 약을 사요 = I buy medicine at the pharmacy

Here, buying happens at that location, so 에서 is correct.

By contrast:

• 에 often marks destination or location of existence
• 약국에 가요 = I go to the pharmacy

So:

• 약국에 가요 = go to the pharmacy
• 약국에서 약을 사요 = buy medicine at the pharmacy

Because 약 is the direct object of 사요 (buy).

• 약을 사요 = buy medicine

The particle 을/를 marks what is being bought, eaten, seen, etc.

So here:

• 약국에서 = where the action happens
• 약을 = what is bought

약 most commonly means medicine in this kind of sentence.

Depending on context, it can also mean things like:

• drug
• pill
• medication
• sometimes even poison in certain compounds or contexts

But with 약국 (pharmacy) and 사요 (buy), learners should understand it here as medicine/medication.

The dictionary form is 사다 (to buy).

In the polite present style:

• 사다 → 사요

So 사요 is the standard polite conversational form.

Compare:

• 사요 = polite, everyday speech
• 삽니다 = polite, more formal
• 사 = casual, plain/informal

And 사요요 is not correct. You only add -요 once.

Korean often leaves out subjects when they are understood from context.

So even though English says I buy medicine, Korean very naturally says:

• 진료가 끝나고 나서 약국에서 약을 사요

The subject I is implied.

If you wanted to include it, you could say:

• 저는 진료가 끝나고 나서 약국에서 약을 사요

But in many real conversations, 저는 would be omitted.

Korean word order is somewhat flexible, but this sentence uses a very natural order.

Standard structure here is:

• [after-clause] + [place] + [object] + [verb]

So:

• 진료가 끝나고 나서 = after the appointment ends
• 약국에서 = at the pharmacy
• 약을 = medicine
• 사요 = buy

You could move some parts for emphasis, but this version is smooth and typical.

It breaks down like this:

• 진료가 = the medical appointment/consultation
• 끝나고 나서 = after it ends
• 약국에서 = at the pharmacy
• 약을 = medicine
• 사요 = buy

So the grammar pattern is essentially:

• [Noun + 가/이] + 끝나고 나서 + [Place + 에서] + [Object + 을/를] + Verb

This is a useful model for making similar sentences, such as:

• 수업이 끝나고 나서 카페에서 커피를 마셔요.
  After class ends, I drink coffee at a café.

By itself, it can be understood either way.

• It could mean a habit/routine:
  After the appointment, I buy medicine at the pharmacy.
• It could also describe a specific situation, depending on context.

Because 사요 is present polite style, Korean often uses it for both:

• general habits
• immediate or near-current actions
• simple neutral statements

If you wanted to make the past explicit, you could say:

• 진료가 끝나고 나서 약국에서 약을 샀어요.
  After the appointment ended, I bought medicine at the pharmacy.