yageul meokgo naseo gamgiga naagago isseoyo.

-고 나서 means after doing X, then Y happens.

So 약을 먹고 나서 means after taking medicine.

It usually emphasizes:

• the first action happens first
• that action is completed
• then the next situation happens

So the sentence is showing a sequence:

1. 약을 먹다 — take medicine
2. 감기가 나아가고 있어요 — the cold is getting better

Because 약 is the direct object of 먹다.

• 약 = medicine
• 먹다 = to eat / take
• 을/를 = object marker

So 약을 먹다 means to take medicine.

If the noun ends in a consonant, Korean uses -을. If it ends in a vowel, Korean uses -를.

Since 약 ends in a consonant, it becomes 약을.

Because 감기 is the subject of 나아가고 있어요.

In Korean, illnesses often act like the subject of verbs such as:

• 낫다 — to recover / heal
• 나아지다 — to improve
• 좋아지다 — to get better

So Korean says something like:

• 감기가 나아요
• 감기가 나아지고 있어요

That is different from English, where we often focus on the person:

• I am getting better
• My cold is getting better

In this sentence, Korean is focusing on the cold as the thing that is improving, so -가 is used.

The verb here is 나아가다, and in this sentence it means to get better / improve.

The form -고 있어요 often shows that something is in progress.

So:

• 나아가요 = gets better / improves
• 나아가고 있어요 = is getting better / is improving

This gives the sense that the cold is not completely gone yet, but it is improving now.

Also, -어요 makes the sentence polite.

Because the sentence describes two different time relationships:

• 약을 먹고 나서 = after taking the medicine
• 감기가 나아가고 있어요 = the cold is getting better now

The first event happened earlier. The second situation is ongoing in the present.

So the sentence means that the medicine was taken first, and now the cold is in the process of improving.

Korean often leaves out the subject when it is obvious from context.

So 약을 먹고 나서 감기가 나아가고 있어요 could mean:

• After I took medicine, my cold is getting better
• After taking medicine, the cold is getting better

Usually, listeners understand who took the medicine from the situation.

This omission of I, you, he, she, and even my is very common in Korean.

Because Korean often leaves out possession when it is already clear.

In English, we naturally say my cold. In Korean, if the speaker is talking about their own condition, just saying 감기가 is usually enough.

So Korean does not need to say something like 저의 감기 unless there is a special reason to emphasize ownership or make a contrast.

This is a very common question.

• 먹고 나서 focuses on sequence: after taking medicine
• 먹어서 often suggests reason/cause: because I took medicine

So:

• 약을 먹고 나서 감기가 나아가고 있어요
  = After taking medicine, my cold is getting better.

• 약을 먹어서 감기가 나아가고 있어요
  = Because I took medicine, my cold is getting better.

In real conversation, the first sentence can still imply that the medicine helped, but grammatically it mainly emphasizes the order of events.

It is understandable, but many learners will more often hear forms like:

• 감기가 나아지고 있어요
• 감기가 좋아지고 있어요

In everyday Korean, 나아지다 is a very common verb for symptoms or conditions improving.

So a very natural alternative would be:

• 약을 먹고 나서 감기가 나아지고 있어요

That said, the original sentence is still understandable and follows the same general idea of gradual improvement.

Yes, but the nuance changes.

• 감기가 나아가고 있어요 puts the focus on the cold as the subject that is improving.
• 감기는 나아가고 있어요 makes the cold the topic, often with a feeling like as for the cold...

For example:

• 열은 아직 있어요. 하지만 감기는 나아가고 있어요.
  = I still have a fever. But as for the cold, it is getting better.

So -가 is the more neutral choice here if you are simply stating the situation.