У меня сильно болит голова.

Russian often expresses possession with the pattern у + genitive + есть / implied existence, rather than with a verb like to have.

So:

• У меня literally means at me
• In natural English, that becomes I have or my ...

In this sentence, У меня сильно болит голова is literally something like:

• At me, the head hurts badly

But natural English is:

• I have a bad headache
• My head hurts badly

This у меня pattern is extremely common in Russian:

• У меня есть машина. = I have a car.
• У меня болит спина. = My back hurts.

So even though English uses my or I have, Russian often uses у меня.

Because у requires the genitive case.

The pronoun я changes like this:

• я = I
• меня = me / of me (genitive or accusative, depending on context)

After у, you must use the genitive:

• у меня = at me / I have
• у тебя = at you / you have
• у него = at him / he has

So у я is impossible. It has to be у меня.

Голова is in the nominative case because it is the grammatical subject of the verb болит.

In Russian, the thing that hurts is usually the subject:

• Голова болит. = The head hurts.
• Спина болит. = The back hurts.
• Рука болит. = The arm hurts.

So in У меня сильно болит голова, the structure is:

• У меня = whose head it is / who is affected
• болит = hurts
• голова = the thing that hurts

Even though English often says I have a headache, Russian is grammatically closer to My head hurts.

In the present tense, Russian verbs agree with the subject in person and number, but not gender.

So with a singular subject, you use the 3rd person singular form:

• голова болит = the head hurts
• рука болит = the arm hurts
• спина болит = the back hurts

The fact that голова is feminine does not change the present-tense form of the verb.

Gender matters mainly in the past tense:

• Голова болела. = My head hurt / The head was hurting
• Глаз болел. = My eye hurt
• Плечо болело. = My shoulder hurt

So болит is correct because голова is singular.

You use болят when the subject is plural.

Compare:

• У меня болит голова. = My head hurts.
• У меня болят глаза. = My eyes hurt.
• У меня болят ноги. = My legs hurt.
• У меня болят зубы. = My teeth hurt.

So the verb changes according to whether the body part is singular or plural:

• singular → болит
• plural → болят

Here сильно means something like:

• badly
• a lot
• severely

With pain, сильно is very natural. It usually sounds better than translating it mechanically as strongly.

So:

• У меня сильно болит голова = My head hurts badly
• У меня сильно болит спина = My back hurts badly

You can think of сильно here as describing the intensity of the pain.

English often uses really, badly, or a lot, while Russian commonly uses сильно.

Yes, очень болит is understandable and natural in many contexts, but сильно болит is especially common when talking about physical pain.

Compare:

• У меня сильно болит голова. = My head hurts badly / severely.
• У меня очень болит голова. = My head hurts very much.

Both work, but сильно often sounds a bit more idiomatic with pain.

A useful rule of thumb:

• сильно = strong intensity, very common with pain
• очень = very, more general intensifier

Because Russian usually does not use the possessive adjective мой / моя / моё / мои for body parts when it is already clear whose body part it is.

Instead, Russian prefers:

• У меня болит голова.
• literally: At me, the head hurts
• naturally: My head hurts

Using моя голова болит is grammatically possible, but it sounds marked or unnatural in a normal situation. It may sound like you are emphasizing my head specifically, perhaps in contrast with someone else’s.

So for ordinary statements about body parts, use:

• У меня болит...
• У него болит...
• У нас болят...

not usually моя / твоя / его unless you specifically want emphasis.

The word order can change, because Russian word order is fairly flexible. The basic meaning stays the same, but the emphasis may shift.

Common versions include:

• У меня сильно болит голова.
• У меня голова сильно болит.
• Голова у меня сильно болит.

The most neutral version is the one you were given:

• У меня сильно болит голова.

Very roughly:

• У меня... first sets up as for me / I have
• putting голова earlier can emphasize the body part
• putting сильно before болит is very natural

So yes, the order can vary, but not every version sounds equally neutral.

Yes, if the context already makes it obvious whose head you mean.

For example:

• Голова болит. = My head hurts / The head hurts.
• Сильно болит голова. = My head hurts badly.

In conversation, Russian often drops information that is already clear.

But if you want to be explicit, especially when first introducing the idea, у меня is very natural:

• У меня болит голова.

So:

• with у меня = clearer, more complete
• without it = more conversational or context-dependent

They are related, but not the same.

У меня сильно болит голова specifically says:

• My head hurts badly
• it names the body part: голова

Мне больно means:

• It hurts
• I’m in pain
• It hurts me

This is more general and does not name the exact body part.

Compare:

• У меня болит голова. = My head hurts.
• Мне больно. = I’m in pain / It hurts.

You can also combine them:

• Мне больно, у меня болит голова.

So if you want to say exactly what hurts, use the болит + body part structure.

In everyday meaning, yes, very often.

Russian У меня болит голова literally means My head hurts, but in many situations English speakers would naturally say:

• I have a headache

So the Russian sentence can correspond to either:

• My head hurts badly
• I have a bad headache

The exact English translation depends on context and style, but the Russian grammar is built around the head hurting, not around having a headache.

The dictionary form is болеть.

Relevant forms:

• болеть = to hurt / to ache / to be ill
• болит = hurts / aches
• болят = hurt / ache (plural)

Examples:

• Голова болит. = The head hurts.
• Зуб болит. = The tooth hurts.
• Зубы болят. = The teeth hurt.

Be aware that болеть can also mean to be ill in some contexts:

• Я болею. = I am ill / I’m sick.

So the verb has a broader range than English hurt alone.