La dentista me dijo que tenía la mejilla un poco hinchada.

Because the sentence is talking about a female dentist.

In Spanish, dentista is commonly used for both men and women, and the article shows the gender:

• el dentista = the male dentist
• la dentista = the female dentist

This is very common with professions ending in -ista:

• el/la turista
• el/la artista
• el/la periodista

So la dentista is completely normal.

Me is the indirect object pronoun, and here it means to me.

So:

• dijo = said / told
• me dijo = told me / said to me

Spanish often uses these little pronouns where English may use a separate word:

• me = to me
• te = to you
• le = to him/her/you
• nos = to us

So La dentista me dijo... literally means The dentist said to me..., but in natural English we usually say The dentist told me...

Dijo is the preterite of decir, and it presents the act of speaking as a completed event.

• La dentista me dijo... = The dentist told me...
  • a finished thing that happened once

If you said decía, that would usually suggest something more ongoing, repeated, or backgrounded:

• La dentista me decía... = The dentist was telling me... / used to tell me...

In this sentence, the speaker is referring to one specific moment when the dentist said something, so dijo is the natural choice.

Here tenía is the imperfect of tener, and it is used because it describes a state at that moment: the cheek was swollen.

The sentence is reporting what the dentist said:

• La dentista me dijo que tenía la mejilla un poco hinchada.

This is like:

• The dentist told me that my cheek was a little swollen.

Spanish often uses the imperfect in reported speech when describing a state that was true at the time of the original statement.

Compare:

• me dijo que tenía... = she told me that I/she had...
• me dijo que tuvo... would sound wrong here, because tuvo is a completed event, not a description of a condition

So tenía fits because having a swollen cheek is a condition, not a one-time completed action.

Grammatically, it can be ambiguous.

La dentista me dijo que tenía la mejilla un poco hinchada could theoretically mean:

1. The dentist told me that I had a slightly swollen cheek.
2. The dentist told me that she had a slightly swollen cheek.

In real life, context usually makes it clear that it means I had the swollen cheek, because a dentist would naturally be commenting on the patient.

If you want to remove the ambiguity, Spanish can make the subject explicit:

• La dentista me dijo que yo tenía la mejilla un poco hinchada.
  = The dentist told me that I had a slightly swollen cheek.

• La dentista me dijo que ella tenía la mejilla un poco hinchada.
  = The dentist told me that she had a slightly swollen cheek.

Spanish often leaves subjects unstated, but that sometimes creates ambiguity like this.

This is a very common Spanish pattern with body parts.

Instead of using a possessive like my, Spanish often uses:

• a definite article (la, el, las, los)
• plus a pronoun that shows whose body part it is

Here, me tells us the person involved, so la mejilla is understood as my cheek.

This kind of structure is extremely common:

• Me duele la cabeza. = My head hurts.
  Literally: The head hurts to me.
• Se lavó las manos. = He washed his hands.
  Literally: He washed the hands to himself.
• Tengo la garganta seca. = My throat is dry.
  Literally: I have the throat dry.

So la mejilla is not strange at all; in fact, it is very natural Spanish.

Because hinchada agrees with la mejilla, which is a feminine singular noun.

• la mejilla = feminine singular
• therefore: hinchada = feminine singular

Agreement is very important in Spanish:

• el ojo hinchado = the swollen eye
• la mejilla hinchada = the swollen cheek
• los ojos hinchados = the swollen eyes
• las mejillas hinchadas = the swollen cheeks

So the adjective changes form to match the noun it describes.

This is a very common Spanish structure:

tener + noun + adjective

It means something like to have something in a certain state.

So:

• tener la mejilla hinchada = to have the cheek swollen
• natural English: to have a swollen cheek

Other examples:

• Tengo el brazo roto. = I have a broken arm.
• Tiene los ojos cerrados. = He/She has his/her eyes closed.
• Tenemos la puerta abierta. = We have the door open.

So in your sentence, tenía la mejilla un poco hinchada means the person had the cheek in a slightly swollen state.

Yes. Tenía hinchada la mejilla is also possible.

Both are correct:

• tenía la mejilla un poco hinchada
• tenía un poco hinchada la mejilla

The version in your sentence is probably the most straightforward and neutral.

Changing the order can slightly change the focus or emphasis, but not the core meaning.

Spanish often uses tener + body part + adjective to describe physical conditions.

So these are natural:

• Tenía la mejilla hinchada.
• Tenía el ojo rojo.
• Tenía la garganta irritada.

You may also hear other ways of expressing similar ideas, such as:

• Tenía la mejilla inflamada.
• Se le había hinchado la mejilla.
• La mejilla estaba un poco hinchada.

But tener la mejilla hinchada is a very normal way to say someone had a swollen cheek.

So it is not that estar would always be impossible; it is just that tener is especially common in this kind of pattern.

Un poco modifies the adjective hinchada and means a little / slightly.

So:

• un poco hinchada = a little swollen / slightly swollen

This placement is natural in Spanish:

• está un poco cansado = he is a little tired
• tenía un poco roja la cara = his face was a bit red
• la mejilla un poco hinchada = the cheek a little swollen

It softens the description. The dentist is not saying it was very swollen, only slightly swollen.

They are similar, but not always identical.

• hinchada = swollen / puffed up
• inflamada = inflamed

In many medical or everyday situations, they can overlap. But the nuance can differ:

• hinchada focuses on swelling
• inflamada can sound a bit more medical and may suggest inflammation, irritation, or infection

So la mejilla un poco hinchada is a very natural everyday way to say the cheek looked slightly swollen.

That version is also correct, but it is direct speech, not reported speech.

Compare:

• Direct speech:
  La dentista me dijo: tienes la mejilla un poco hinchada.
  = The dentist told me, Your cheek is a little swollen.

• Reported speech:
  La dentista me dijo que tenía la mejilla un poco hinchada.
  = The dentist told me that my cheek was a little swollen.

In reported speech, Spanish often shifts the tense back:

• tienes → tenía

That is why the sentence uses que tenía.

Yes, and it means something slightly different in nuance.

• me dijo que tenía la mejilla un poco hinchada
  focuses on the state: my cheek was swollen

• me dijo que se me había hinchado la mejilla
  focuses more on the change/process: my cheek had swollen up

That second version is also very natural Spanish, especially if the idea is that the swelling had developed recently.

So the original sentence describes the condition; this alternative highlights how it happened.

Yes, pretty much.

La mejilla means the cheek, especially the fleshy part of the face.

Some useful related words:

• mejilla = cheek
• cara = face
• mandíbula = jaw
• encía = gum
• muela / diente = tooth

In a dental context, mejilla is exactly the kind of word you would expect to hear.

Yes, it sounds natural in Spain.

A speaker in Spain might also say similar things such as:

• La dentista me dijo que tenía la mejilla un poco inflamada.
• La dentista me dijo que se me había hinchado un poco la mejilla.

But your original sentence is perfectly natural and idiomatic.