Après le sport, mon épaule droite et mon genou gauche sont un peu gonflés.

Because épaule is a feminine noun, you would normally expect ma. But in French, ma, ta, and sa change to mon, ton, and son before a word that starts with a vowel or a mute h.

So:

• ma main
• mon épaule

This is done for ease of pronunciation. It does not make épaule masculine; the noun is still feminine.

In French, many adjectives come after the noun, and words like droit/droite and gauche usually do when they describe body sides.

So:

• l’épaule droite = the right shoulder
• le genou gauche = the left knee

This is normal French word order. English often puts these words before the noun, but French usually puts them after.

Because adjectives must agree with the noun they describe.

• épaule is feminine singular, so droit becomes droite
• genou is masculine singular, so gauche stays in its basic form

Some adjectives change visibly for feminine forms, and some do not.

Examples:

• droit → droite
• petit → petite
• but gauche → gauche in both masculine and feminine singular

Because each singular noun normally needs its own determiner in French.

So you say:

• mon épaule droite et mon genou gauche

not usually:

• mon épaule droite et genou gauche

French generally repeats the possessive adjective with each noun unless the structure is clearly different.

Because the subject is plural: mon épaule droite et mon genou gauche refers to two things.

So French uses the plural form of être:

• est = is
• sont = are

Since both the shoulder and the knee are being described, the verb must be plural.

Because gonflés agrees with the full subject: mon épaule droite et mon genou gauche.

This subject is:

• plural, because there are two body parts
• mixed gender, because épaule is feminine and genou is masculine

In French, when adjectives describe a mixed group, the agreement is normally masculine plural.

So:

• singular masculine: gonflé
• singular feminine: gonflée
• plural masculine (or mixed): gonflés
• plural feminine: gonflées

That is why the sentence uses gonflés.

Un peu means a little or slightly. It softens the description.

So:

• gonflés = swollen
• un peu gonflés = a little swollen / slightly swollen

It comes before the adjective or past participle it modifies. This is a very common expression in French.

Après le sport means after sport / after exercising / after sports activity in a general sense.

French often uses le + noun to talk about an activity in a general way:

• j’aime le sport
• après le sport

Du sport would more naturally appear in expressions like:

• faire du sport = to do sport / to exercise

So:

• faire du sport
• but après le sport

Both involve sport, but the article changes depending on the structure.

Usually it means exercise or sports activity in general, depending on context.

So Après le sport can be understood as:

• after exercise
• after playing sports
• after a workout

French often uses le sport broadly, not only for one specific game or discipline.

French does often use definite articles with body parts, especially in constructions like:

• J’ai mal à l’épaule.
• Je me suis blessé le genou.

But in this sentence, the speaker is simply identifying which body parts are swollen, so using mon is completely natural:

• mon épaule droite
• mon genou gauche

This makes the ownership explicit and sounds very normal in this kind of descriptive statement.

Yes. Gonflé literally suggests something that is swollen, puffed up, or inflated. In a body-related context, swollen is usually the best choice.

Depending on context, it can suggest:

• swollen
• puffy
• a bit inflamed-looking

Here, with a shoulder and a knee after sport, swollen is the most natural interpretation.

Then the subject would be singular, so both the verb and adjective would be singular too.

For example:

• Après le sport, mon épaule droite est un peu gonflée.

Changes:

• sont → est
• gonflés → gonflée

Because épaule is feminine singular.

A few points may be useful:

• Après: the final s is normally silent
• épaule: starts with a vowel sound, which is why you get mon épaule
• genou: the g is soft, like the j in measure
• sont un peu may involve smooth linking in natural speech, though the main thing is just to keep the flow natural
• gonflés: the final s is silent

So even though several words have written final consonants, many of them are not pronounced.