Moje dcera má rýmu, ale jinak se cítí dobře.

Because mít takes a direct object, and that object goes in the accusative case.

The dictionary form is rýma (nominative), but after má you need the accusative singular: rýmu.

So:

• rýma = nominative
• rýmu = accusative

This is very common with illnesses in Czech:

• mám kašel
• má horečku
• má rýmu

In Czech, many common illnesses are expressed with mít + noun, just like English often says have:

• mám rýmu
• mám kašel
• mám horečku

So Moje dcera má rýmu is a completely natural way to say that your daughter has a cold/runny nose.

Czech can also use other expressions for being sick in general, such as je nemocná, but má rýmu is more specific.

Here jinak means otherwise, apart from that, or in other respects.

So:

Moje dcera má rýmu, ale jinak se cítí dobře.
= She has a cold/runny nose, but otherwise she feels fine.

It helps soften the first statement and shows that this is the only problem being mentioned.

Because the usual Czech expression for to feel in the sense of to feel well/bad/tired is cítit se.

Compare:

• cítit = to feel/sense something
  
  • Cítím bolest. = I feel pain.
• cítit se = to feel, to be feeling
  
  • Cítím se dobře. = I feel well/fine.

So in your sentence, se cítí dobře means feels fine.

Because Czech normally uses an adverb after cítit se:

• cítí se dobře
• cítí se špatně
• cítí se skvěle

So dobře is the correct form here.

Dobrá is an adjective, and it would need to agree with a noun. That is not the pattern used with cítit se in this meaning.

Yes, you could say Dcera má rýmu, but it depends on context.

Czech often leaves out possessives when the relationship is obvious. However, moje is very natural when:

• you are introducing the person,
• you want to be clear,
• or you want a slight emphasis on my daughter.

So both are possible, but Moje dcera má rýmu... is a very normal full sentence.

Both verbs are in the 3rd person singular, which matches dcera.

• má = has
• cítí se = feels

Czech does not need to repeat the subject in the second clause if it is still the same subject. English does the same thing:

• My daughter has a cold, but otherwise feels fine.

The subject is still my daughter throughout.

Yes, cítí se dobře is also correct.

The reason is that se is a clitic in Czech, and clitics usually go in the second position in their clause.

In the second clause here, the first element is jinak, so se comes right after it:

• ale jinak se cítí dobře

But if the verb starts the clause, then you get:

• Cítí se dobře.

So:

• Jinak se cítí dobře. ✓
• Cítí se dobře. ✓
• Jinak cítí se dobře. ✗ unnatural

Czech word order is fairly flexible, but some versions sound more natural than others.

The original sentence is a very natural, neutral version:

Moje dcera má rýmu, ale jinak se cítí dobře.

You may also hear slight variations, for example if the speaker wants to emphasize a different part of the sentence. But for a learner, this version is an excellent pattern to remember.

A good rule is:

• keep má rýmu together,
• use cítit se dobře as a set phrase,
• and remember that se usually comes early in the clause.