Lekar će proveriti da li imam alergiju.

The future here is će proveriti = will check.

It is made of:

• će = the 3rd person singular future auxiliary, from hteti
• proveriti = the infinitive to check

So:

• ja ću proveriti = I will check
• ti ćeš proveriti = you will check
• on/ona će proveriti = he/she will check

Because lekar is singular, you use će.

Yes. će is a clitic, so it often comes in the second position of the clause.

That is why you get:

• Lekar će proveriti... = The doctor will check...

If the verb comes first, Serbian often joins the future auxiliary to the verb:

• Proveriće da li imam alergiju.

Both are correct. But in a sentence with a subject first, Lekar će proveriti is the normal pattern.

A learner should avoid forms like Lekar proveriće... in neutral standard usage.

Here da li means whether / if and introduces an indirect yes-no question.

So:

• Da li imam alergiju? = Do I have an allergy?
• Lekar će proveriti da li imam alergiju. = The doctor will check whether I have an allergy.

It does not mean that here. It specifically marks the idea of checking the answer to a yes/no question.

Because Serbian, like English here, uses the present tense in the embedded clause:

• da li imam alergiju = whether I have an allergy

The checking happens in the future, but the clause after da li expresses the condition being checked. In English you also say will check whether I have, not whether I will have.

You would use a future form only if the meaning were really about a future allergy state, for example:

• da li ću imati alergiju = whether I will have an allergy

But that is not the normal meaning in this sentence.

Because Serbian usually drops subject pronouns when they are not needed.

The verb form imam already tells you the subject is I:

• imam = I have

So da li imam alergiju naturally means whether I have an allergy.

You can add ja for emphasis or contrast:

• da li ja imam alergiju = whether I have an allergy

That sounds more marked, as if you are contrasting yourself with someone else.

Because imati takes a direct object, and the direct object here is in the accusative case.

The noun is:

• nominative: alergija
• accusative singular: alergiju

So:

• Imam alergiju. = I have an allergy.
• Alergija je ozbiljna. = The allergy is serious.

This is a very common pattern with feminine nouns ending in -a:

• knjiga → knjigu
• kafa → kafu
• alergija → alergiju

It can mean either, depending on context.

Serbian has no articles, so there is no separate word for a or the. The listener understands it from the situation.

So Lekar će proveriti... could mean:

• The doctor will check...
• A doctor will check...

In many real contexts, English would probably translate it as the doctor.

This is about aspect, which is very important in Serbian.

• proveriti = perfective, a completed check
• proveravati = imperfective, repeated or ongoing checking

In this sentence, the doctor is expected to do a single check and reach a result, so proveriti is the natural choice.

Compare:

• Lekar će proveriti... = The doctor will check...
• Lekar će proveravati... = The doctor will be checking / will check repeatedly...

So proveriti fits better here.

Yes. In Serbian, especially in everyday speech, you can often use:

• će + infinitive
  or
• će da + present

So both are possible:

• Lekar će proveriti da li imam alergiju.
• Lekar će da proveri da li imam alergiju.

The first version is very standard and compact. The second is also very common in spoken Serbian.

Just note that će da + present is especially typical of Serbian; learners will see it a lot in conversation.

Yes. Both can refer to a doctor, but they are not always used in exactly the same way.

• lekar = doctor, physician; a standard and very neutral word
• doktor = also very common in everyday speech

In many situations, they can replace each other:

• Lekar će proveriti...
• Doktor će proveriti...

A small nuance:

• doktor can also mean someone with a doctorate, depending on context
• lekar specifically means a medical doctor

So in medical contexts, both are fine, but lekar is especially precise.

Yes.

This sentence is in standard Serbian with Ekavian pronunciation/spelling:

• lekar
• proveriti

In other regional standards, you may see:

• lijekar instead of lekar
• provjeriti instead of proveriti

So related variants include:

• Ljekar će provjeriti da li imam alergiju.
• Liječnik će provjeriti da li imam alergiju.

These are not different in meaning; they reflect regional or standard-language differences across Serbian/Croatian/Bosnian/Montenegrin usage.