Jeg har tandpine, og tandbylden bliver større.

In Danish, many illnesses, symptoms, and conditions are expressed with har + noun without an article.

So:

• jeg har tandpine = I have toothache
• jeg har feber = I have a fever / I have fever
• jeg har influenza = I have the flu

Using en here would usually sound unnatural. Tandpine is treated more like a general condition than a countable object.

Tandpine is a compound noun:

• tand = tooth
• pine = pain

So it literally means tooth-pain, which corresponds to toothache in English.

Danish makes compound words very freely, so it is useful to get used to reading them as smaller parts joined together.

Tandbylden means the dental abscess or the tooth abscess.

It breaks down like this:

• tand = tooth
• byld = abscess, boil
• -en = the definite ending for a common-gender singular noun

So:

• en tandbyld = a tooth abscess
• tandbylden = the tooth abscess

This is a very important feature of Danish: instead of putting the in front of the noun, Danish often adds the definite article as an ending.

Compare:

• en bil = a car
• bilen = the car

Because they are being used differently.

• tandpine is a general condition: I have toothache
• tandbylden refers to a specific thing: the abscess

So in the sentence:

• jeg har tandpine = I have toothache
• tandbylden bliver større = the abscess is getting bigger

The first noun is non-specific and condition-like; the second points to a particular physical object/problem.

Because bliver means becomes / gets, while er means is.

So:

• tandbylden er større = the abscess is bigger
• tandbylden bliver større = the abscess is getting bigger / becoming bigger

In your sentence, the idea is that the abscess is changing in size, so bliver is the natural choice.

In Danish, many common adjectives form the comparative with a special ending rather than with a separate word.

• stor = big
• større = bigger
• størst = biggest

So:

• stor → større

This is like English big → bigger, not more big.

The sentence has two main clauses joined by og = and:

1. Jeg har tandpine
2. tandbylden bliver større

Basic Danish main-clause word order is usually:

• subject + verb + ...

So here:

• Jeg = subject
• har = verb
• tandpine = object/complement

and:

• tandbylden = subject
• bliver = verb
• større = complement

This is very similar to normal English word order.

Yes, jeg har ondt i tanden is also possible, but it is slightly different in feel.

• jeg har tandpine = I have toothache
• jeg har ondt i tanden = I have pain in my tooth / my tooth hurts

The first is a standard noun expression for the condition.
The second describes the pain more directly.

Both are natural, but tandpine is especially common when talking about the problem in a general medical sense.

A rough guide is:

• tand ≈ tan (the d is often very soft or barely heard)
• byld has a front rounded vowel that English does not really have
• -en is a very light ending

A rough English-friendly approximation might be: TAN-bül-den
—but this is only approximate.

A few pronunciation points:

• Danish y in byld is not like English y. It is closer to a rounded vowel made with the tongue position of ee but with rounded lips.
• Final consonants can sound softer than an English speaker expects.
• The unstressed -en ending is usually reduced.

If you are learning pronunciation, byld is probably the hardest part of the sentence.

Og simply means and, and yes, it commonly joins two full clauses.

So:

• Jeg har tandpine = I have toothache
• og tandbylden bliver større = and the abscess is getting bigger

This is completely normal Danish. Just like in English, og can connect:

• words
• phrases
• whole clauses

Yes. Danish uses compound nouns very heavily, just like German and often more than English.

Examples:

• tandlæge = dentist (tooth-doctor)
• hovedpine = headache (head-pain)
• ørepine = earache (ear-pain)
• tandbørste = toothbrush (tooth-brush)

So if you can identify the parts of a compound, you can often guess the meaning. That is a very useful reading skill in Danish.

Yes.

• har = present tense of at have = to have
• bliver = present tense of at blive = to become / get

So the whole sentence describes a current situation:

• I have toothache
• the abscess is getting bigger

It is not past tense and not future tense.