isya ni kaze da to sindansareta node, kaeri ni igusuri de ha naku, seki no kusuri wo katta.

Because 診断された is passive: was diagnosed.

In Japanese passives, the person who performs the action is often marked with に. So:

• 医者に診断された = was diagnosed by a doctor

If this were active instead, you would expect something like:

• 医者が診断した = the doctor diagnosed ...

So 医者に does not mean to the doctor here; it means by the doctor.

と is marking the content of the diagnosis: what the doctor diagnosed it as.

Because 風邪 is a noun, when you state it is a cold, the plain copula だ is used:

• 風邪だ = it is a cold

Then that whole statement is followed by と:

• 風邪だと診断された = was diagnosed as having a cold / was diagnosed with a cold

So だ is there because the quoted/thought content is a noun sentence.

You may also sometimes see 風邪と診断された, but 風邪だと makes the underlying statement more explicit.

The passive is natural here because the sentence is focusing on the person who received the diagnosis, not on the doctor.

• 医者が風邪だと診断した = The doctor diagnosed ...
• 医者に風邪だと診断された = (I/they) was/were diagnosed with a cold by the doctor

In English, I was diagnosed with a cold is also very natural, so the Japanese passive works similarly here.

It also lets Japanese omit the patient more easily, since the speaker is probably understood from context.

Here ので means because or since.

• 診断されたので、...買った = Because I was diagnosed..., I bought ...

Compared with から, ので often sounds a bit:

• softer
• more explanatory
• more objective

So ので fits well when giving a reason in a calm, matter-of-fact way.

帰り means the return, the way back, or the trip home.

With に, it becomes a time/occasion expression:

• 帰りに = on the way back / on the way home

So in this sentence, it means the speaker bought the medicine while returning, probably from the doctor or clinic.

It modifies 買った.

The meaning is:

• Because I was diagnosed with a cold by the doctor, on the way back I bought cough medicine...

It would not naturally mean I was diagnosed on the way back in this sentence. Semantically and structurally, 帰りに goes with the buying.

This is the pattern:

• Aではなく、B = not A, but B
• Aではなく、Bを買った = bought B instead of A

So:

• 胃薬ではなく、せきの薬を買った
• I bought cough medicine, not stomach medicine
• I bought cough medicine instead of stomach medicine

The は inside ではなく adds contrast. It highlights the rejection of 胃薬 in favor of something else.

A more casual version would often be:

• 胃薬じゃなくて、せきの薬を買った

Because Japanese uses both fixed compound words and XのY phrases, depending on what sounds natural.

• 胃薬 is a very common fixed word meaning stomach medicine
• せきの薬 literally means medicine for cough

For cough medicine, Japanese often says things like:

• せきの薬
• 咳止め

So the difference is mostly lexical/natural usage, not a grammar problem.

The kanji is 咳, but it is very often written in kana as せき.

This happens a lot in Japanese when:

• the kanji is relatively less common or harder
• the writing wants to feel easier to read
• the word is common enough that kana looks natural

So せきの薬 is completely normal.

Because Japanese often omits information that is obvious from context.

In this sentence, the understood subject is probably I:

• (私は) 医者に風邪だと診断されたので、...買った。

Japanese does this very often with subjects, objects, and other elements when the listener can easily infer them.

So even though I is not stated, the sentence still sounds complete and natural.

The whole sentence is written in plain style:

• 診断された
• 買った

So that part is straightforward.

As for 風邪だと, when と quotes or marks content, Japanese normally uses the plain form inside that content:

• 風邪だ = plain
• 風邪です = polite

So 風邪だと診断された is the normal form here.

Even in a polite sentence, the quoted content often still stays plain:

• 医者に風邪だと診断されたので、せきの薬を買いました。

That is normal Japanese.