Hun fik også en vaccine sidste år, fordi hun ofte bliver syg om vinteren.

Fik is the past tense of at få, which means to get or to receive.

This verb is irregular:

• infinitive: at få
• present: får
• past: fik
• past participle: fået

So hun fik en vaccine means she got a vaccine.

In a normal Danish main clause, the finite verb usually comes in second position. This is often called the V2 rule.

So in:

• Hun = first element
• fik = second element
• også comes after that

That is why you get Hun fik også en vaccine...

If you moved another element to the front, the verb would still stay second:

• Sidste år fik hun også en vaccine.

Because vaccine is a common-gender noun in Danish, so it takes en.

Danish nouns are usually either:

• en-words (common gender)
• et-words (neuter)

So:

• en vaccine = a vaccine
• vaccinen = the vaccine

You simply have to learn the gender with the noun.

Danish often uses time expressions like sidste år, sidste uge, næste måned, and i går without a preposition.

So:

• sidste år = last year
• not i sidste år

This works very much like English, where we also say last year, not in last year.

Bliver syg means gets sick / becomes ill, while er syg means is sick.

So the sentence suggests a repeated event:

• hun ofte bliver syg om vinteren = she often gets sick in winter

If you said hun ofte er syg om vinteren, it would focus more on her state of being ill during winter, not so much on becoming ill.

Om vinteren is the normal way to say in winter or during the winter when you mean it generally or habitually.

So:

• om vinteren = in winter, during winter in general

This fits the sentence because it describes something that happens regularly.

By contrast, i vinter usually means this winter.
And i vinteren is generally not the natural choice here.

Because fordi introduces a subordinate clause.

After fordi, Danish does not use main-clause inversion. You keep the subject before the verb:

• fordi hun...
• not fordi bliver hun...

Also, adverbs like ofte are very naturally placed before the finite verb in this kind of clause:

• fordi hun ofte bliver syg

So the word order is normal Danish subordinate-clause word order.

Here syg is a predicative adjective after bliver.

With a singular subject like hun, the basic form is used:

• hun er syg
• hun bliver syg

You would see syge with a plural subject:

• de er syge
• de bliver syge

So syg is correct because the subject is singular.

The comma separates the main clause from the subordinate clause:

• Hun fik også en vaccine sidste år
• fordi hun ofte bliver syg om vinteren

In Danish, many writers put a comma before a clause introduced by fordi. That is very common and standard-looking.

You may also sometimes see sentences without that comma, depending on comma style, but the comma in your sentence is completely normal.