A dentista explicou que, se meu lábio continuar inchado amanhã, eu devo voltar à clínica.

Yes. Dentista is one of those profession nouns that often keeps the same form for both genders.

• a dentista = the female dentist
• o dentista = the male dentist

So the article shows the gender, not the ending of the noun itself.

The comma separates the inserted conditional clause:

• se meu lábio continuar inchado amanhã

The basic structure is:

• A dentista explicou que eu devo voltar à clínica.

Then the speaker inserts the condition:

• A dentista explicou que, se meu lábio continuar inchado amanhã, eu devo voltar à clínica.

In Portuguese, when a subordinate clause like this is inserted in the middle, commas are normally used to mark it off.

Because se means if, and this is a condition, not a certainty.

• se meu lábio continuar inchado amanhã = if my lip is still swollen tomorrow

If you used quando, it would sound more like when, implying the speaker expects it to happen. Here the dentist is talking about a possibility, so se is the right choice.

Here, continuar is not an infinitive in function. It is the future subjunctive, which is very common after se when talking about a future possibility.

Pattern:

• se + future subjunctive

So:

• se meu lábio continuar inchado amanhã = if my lip remains swollen tomorrow

For many -ar verbs, the future subjunctive form for ele/ela/você looks exactly like the infinitive:

• infinitive: continuar
• future subjunctive (eu/ele/ela/você): continuar

That is why it looks confusing.

Inchado means swollen. It is acting like an adjective here.

Since it describes lábio, it agrees with that noun:

• lábio = masculine singular
• so: inchado = masculine singular

If the noun were feminine, it would change:

• a boca inchada = the swollen mouth

Portuguese often uses possessives where English might or might not.

• meu lábio = my lip

This makes the sentence very clear and natural. Using o lábio could also be understandable in some contexts, especially when it is obvious whose lip is being discussed, but meu lábio is more explicit.

Yes. In Brazilian Portuguese, possessives can appear with or without the definite article:

• meu lábio
• o meu lábio

Both are possible. In Brazil, the version without the article is very common and natural in many contexts, especially in straightforward speech like this.

Yes, subject pronouns are often optional in Portuguese because the verb form already shows the person:

• devo voltar = I should/must return
• eu devo voltar = same meaning, but with the subject stated

The pronoun eu may be included for:

• clarity
• emphasis
• rhythm
• contrast

In a longer sentence like this, saying eu can make it easier to follow.

It can cover all of those ideas depending on context.

• dever often expresses obligation, recommendation, or expectation.
• In a medical context, eu devo voltar à clínica usually sounds like advice with some force behind it.

Natural English equivalents could be:

• I should go back to the clinic
• I need to go back to the clinic
• I’m supposed to go back to the clinic

So it is stronger than a casual suggestion, but not always as harsh as an absolute command.

À is a contraction of:

• a = the preposition to
• a = the feminine singular article the

So:

• voltar a a clínica → voltar à clínica

This is called crase in Portuguese.

Since clínica is feminine and the phrase requires the preposition a, they combine into à.

So:

• à clínica = to the clinic

Yes, you could. In Brazilian Portuguese, both are possible:

• voltar à clínica
• voltar para a clínica

The version with à is a bit more compact and somewhat more formal or written-sounding.
The version with para a is very common in everyday speech.

Because amanhã is modifying the whole condition: whether the lip is still swollen tomorrow.

• se meu lábio continuar inchado amanhã

This word order is very natural in Portuguese. You could move amanhã in some cases, but the original version sounds smooth and standard.

For example:

• se amanhã meu lábio continuar inchado
  also works, but it shifts the focus slightly toward tomorrow.

Because after se referring to a future condition, Portuguese normally uses the future subjunctive, not the present subjunctive.

Compare:

• Espero que meu lábio continue inchado.
  = I hope my lip stays swollen.
  Here continue is present subjunctive after espero que.

• Se meu lábio continuar inchado amanhã...
  = If my lip is still swollen tomorrow...
  Here continuar is future subjunctive after se.

So both forms exist, but they are used in different structures.

Because the explaining happened in the past, but the instruction is still valid now and for the future.

• A dentista explicou = the act of explaining happened already
• eu devo voltar = the obligation/advice still applies

This is very normal in Portuguese. The tense of the reported statement depends on the meaning, not just on the tense of the reporting verb.