После долгой тренировки у меня заболела спина.

Because после always requires the genitive case.

• тренировка → genitive singular тренировки
• долгая → it must agree with тренировка, so it also becomes genitive singular feminine: долгой

So:

• после тренировки = after the workout / after training
• после долгой тренировки = after a long workout

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после долгого дня = after a long day

Russian very often uses у + genitive to talk about states, sensations, and things happening to a person, especially with body parts and health.

So у меня заболела спина literally feels like:

• at me / with me, the back started to hurt

This is much more natural in Russian than saying моя спина заболела.

Why? Because Russian usually does not emphasize ownership with body parts unless there is a special reason. In English we say my back hurts, but in Russian the natural way is often:

• У меня болит голова = My head hurts
• У меня болят ноги = My legs hurt
• У меня заболела спина = My back started hurting

Моя спина заболела is grammatically possible, but it sounds less natural in an ordinary everyday context and may sound oddly emphatic.

У меня is the preposition у plus the genitive form of я:

• я = I
• меня = me / of me (genitive or accusative form depending on context)
• у меня = at me / by me / with me

In this sentence, у меня does not mean physical location. It marks the person affected.

So in sentences about pain, illness, feelings, or possession, у меня is extremely common:

• У меня есть брат. = I have a brother.
• У меня температура. = I have a fever.
• У меня болит горло. = My throat hurts.

Here it means something like as for me or in my case: my back started hurting.

Because the verb agrees with спина, which is a feminine singular noun.

In the Russian past tense, verbs usually agree in gender and number with the grammatical subject:

• masculine: заболел
• feminine: заболела
• neuter: заболело
• plural: заболели

Here, the subject is спина:

• спина = back
• it is feminine singular
• so the verb is заболела

Compare:

• У меня заболел зуб. = My tooth started hurting.
  (зуб is masculine)
• У меня заболело горло. = My throat started hurting.
  (горло is neuter)
• У меня заболели ноги. = My legs started hurting.
  (ноги is plural)

This is an aspect question.

• болеть = to hurt / to be hurting / to ache
• заболеть = to start hurting, to fall ill, to become painful

So:

• У меня болела спина. = My back was hurting / used to hurt.
• У меня заболела спина. = My back started hurting.

In your sentence, заболела suggests the pain began after the workout. That is why it fits well with после долгой тренировки.

So the sentence is not just describing a general condition; it marks the onset of pain.

No. It can mean slightly different things depending on the subject.

With a person, it often means to fall ill / get sick:

• Я заболел. = I got sick.

With a body part, it often means to start hurting:

• У меня заболела голова. = My head started hurting.
• У меня заболела спина. = My back started hurting.

So in this sentence, it does not mean the back became medically ill in a broad sense. It means it began to hurt.

Because Russian often leaves possession understood when talking about body parts, especially if the owner is already clear from the context.

In English, we usually say:

• my back
• my head
• my arm

In Russian, it is much more natural to say:

• У меня болит спина
• У меня болит голова
• У меня болит рука

The possession is already clear from у меня, so adding моя would usually be unnecessary.

Yes. Russian word order is fairly flexible, because case endings show the grammatical relationships.

The neutral version here is:

• После долгой тренировки у меня заболела спина.

But you could also say:

• У меня после долгой тренировки заболела спина.
• Спина у меня заболела после долгой тренировки.

These versions are all understandable, but the emphasis changes a bit.

• После долгой тренировки... puts the time/background first.
• У меня... puts the affected person first.
• Спина... puts focus on the body part.

For a normal statement, the original sentence sounds very natural.

Because the subject of the sentence is not I. The grammatical subject is спина.

English says:

• My back started hurting

Russian structures it as:

• At me / for me, the back started hurting

So у меня refers to the person affected, but it is not the subject. The subject is спина, which is why the verb agrees with спина and not with я.

It is not grammatically wrong, but it is less natural in ordinary speech.

Моя спина заболела sounds more marked, as if you are stressing my back specifically, perhaps in contrast to someone else’s, or for stylistic emphasis.

In everyday Russian, speakers usually prefer:

• У меня заболела спина

So if your goal is natural spoken Russian, the version with у меня is the better choice.

In this sentence, тренировки is genitive singular of тренировка, so it most naturally means after a long workout / after a long training session.

If you wanted to talk about training in a broader or repeated sense, Russian might use other wording depending on the meaning, for example:

• после тренировок = after training sessions / after workouts
• после долгих тренировок = after long training sessions

So the singular here suggests one specific long session.