После прогулки под дождём у меня пропал аппетит и начался озноб.

Because после requires the genitive case.

• прогулка = a walk
• Genitive singular: прогулки

So:

• после прогулки = after the walk / after a walk

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после дождя = after the rain

Literally, под дождём means under the rain, but in natural English we usually say in the rain.

In Russian, под can be used with the instrumental case to mean being under something physically or within its effect:

• под столом = under the table
• под солнцем = under the sun
• под дождём = in/under the rain

Here, дождь becomes дождём, which is the instrumental singular form.

So the phrase прогулка под дождём means a walk in the rain.

Russian often uses у + genitive to express that something happens to a person or is experienced by a person, especially with physical states, illnesses, sensations, or possessions.

• у меня literally means by me / at me
• In context, it often works like I have, to me, or for me

So:

• у меня пропал аппетит = literally my appetite disappeared on me
• natural English: I lost my appetite

This pattern is very common:

• у меня болит голова = I have a headache
• у меня температура = I have a fever
• у меня начался кашель = I started coughing / I developed a cough

Yes, you could. Я потерял аппетит is grammatical and understandable.

But there is a nuance:

• я потерял аппетит = I lost my appetite
• у меня пропал аппетит = my appetite disappeared / I lost my appetite

The version in your sentence sounds a bit more natural for describing a physical condition that came on by itself. It focuses on the state change, not on your action.

So both are possible, but у меня пропал аппетит often sounds more idiomatic in health-related contexts.

Because пропал agrees with аппетит, and аппетит is a masculine singular noun.

Russian past tense verbs agree with the subject in gender and number:

• masculine: пропал
• feminine: пропала
• neuter: пропало
• plural: пропали

Examples:

• аппетит пропал — appetite disappeared
• надежда пропала — hope disappeared
• желание пропало — desire disappeared

So пропал is used because аппетит is masculine.

Начался is the past tense of начаться, which means to begin / to start.

So:

• начался озноб = chills began
• natural English: I started having chills or I got chills

Again, the subject is озноб, so the verb agrees with it:

• озноб is masculine singular
• therefore: начался

This is a common way to describe symptoms in Russian:

• у меня начался кашель = I started coughing / I developed a cough
• у меня началась температура = I developed a fever
• у меня началась боль = pain started

Озно́б means chills, shivering, or a feeling of shaking from cold or illness.

It does not mean exactly the same thing as fever.

So:

• озноб = chills / shivering
• температура = fever / elevated temperature

In this sentence, it suggests that after being out in the rain, the speaker began to feel physically unwell and got chills.

Both are normal Russian ways to describe what happened to the speaker.

You could think of both nouns as the real grammatical subjects:

• аппетит пропал = appetite disappeared
• озноб начался = chills began

And у меня tells you for whom this happened.

So the whole sentence is built around two events:

1. аппетит пропал
2. озноб начался

Both happened у меня = to me / in my case

Russian often prefers this kind of structure when talking about bodily states or symptoms.

Because in Russian, a short adverbial phrase at the beginning of a sentence usually does not need a comma.

So this is normal:

• После прогулки под дождём у меня пропал аппетит...

A comma might appear in some cases for emphasis or if the phrase is especially long or parenthetical, but in an ordinary sentence like this, no comma is standard.

Yes. Russian word order is flexible, and changing it mostly changes emphasis, not the core meaning.

For example:

• После прогулки под дождём у меня пропал аппетит и начался озноб.
• У меня после прогулки под дождём пропал аппетит и начался озноб.
• Аппетит у меня после прогулки под дождём пропал, и начался озноб.

The original version sounds natural and neutral: it first gives the time/circumstance, then says what happened.

In careful writing, дождём with ё is best, because that is the correct pronunciation and form.

However, in many Russian texts, ё is often replaced by е, so you may also see:

• дождем

Native speakers usually understand it from context. But for learners, using ё is helpful because it shows the correct stress and pronunciation more clearly.

They are close, but прогулка под дождём is the more natural expression for a walk in the rain.

• под дождём emphasizes being out while the rain is falling on you
• в дождь can mean during rainy weather or when it was raining, but it is less vivid here

So for this sentence, после прогулки под дождём is a very idiomatic choice.