Die Wunde an meinem Knie ist klein, aber mein Ellbogen tut auch weh.

Because German nouns have grammatical gender:

• die Wunde = feminine
• der Ellbogen = masculine
• das Knie = neuter

That affects the article and other words around the noun:

• die Wunde
• mein Ellbogen
• mein Knie

Notice that mein can be used with masculine and neuter nouns in the nominative singular, so both mein Ellbogen and mein Knie look the same there.

Because an can take either the accusative or the dative, depending on meaning.

Here it means location: on / at my knee, so German uses the dative.

• an meinem Knie = at/on my knee

If there were movement toward something, accusative would be possible in other contexts, but not here.

Also, mein changes in the dative neuter:

• nominative: mein Knie
• dative: meinem Knie

Because Knie is in the dative case after an in this sentence.

The possessive determiner mein changes its ending depending on gender, number, and case.

For neuter singular:

• nominative: mein Knie
• dative: meinem Knie

So:

• an meinem Knie is correct

This is a very common pattern in German.

German often uses a possessive with body parts, just like English, so meinem Knie is completely normal.

But the structure is a little different because German is expressing the idea as the wound at/on my knee:

• die Wunde an meinem Knie

That is a very natural German way to describe where the wound is.

You could think of it as:

• the wound on my knee

So the important thing is not that German avoids the possessive here, but that it uses the prepositional phrase an meinem Knie to specify location.

Because klein comes after the verb ist, so it is acting as a predicate adjective.

In German, predicate adjectives do not take endings:

• Die Wunde ist klein.
• Der Ellbogen ist schlimm verletzt.
• Das Knie ist rot.

Adjective endings are used when the adjective comes before the noun:

• eine kleine Wunde

So:

• die Wunde ist klein = correct
• die kleine Wunde = also correct, but different structure

wehtun is a separable verb meaning to hurt / to be painful.

In a normal present-tense sentence, it splits:

• mein Ellbogen tut weh

The verb works like this:

• infinitive: wehtun
• er/sie/es form: tut weh

Examples:

• Mein Kopf tut weh.
• Der Rücken tut weh.

In a clause with another verb, it stays together at the end:

• Mein Ellbogen wird wehtun.
• Es kann wehtun.

So tut weh is just the separated form of wehtun.

Because in German, the body part itself is usually the subject with wehtun.

So German commonly says:

• Mein Ellbogen tut weh.
  literally: My elbow hurts

Rather than:

• I hurt at the elbow

English can say My elbow hurts, and German strongly prefers that structure here.

You can also say:

• Mir tut der Ellbogen weh.

That literally means something like To me, the elbow hurts, and it is also very common.

auch means also / too.

Here it adds the idea that in addition to the wound being small, the elbow hurts as well:

• aber mein Ellbogen tut auch weh

The placement of auch is fairly natural here because it modifies the idea of weh tun:

• tut auch weh = also hurts

In English, also can move around a bit. German is a little stricter about word order, but this placement is very common and natural.

Because German main clauses usually follow the verb-second rule.

First clause:

• Die Wunde / ist / klein

Second clause:

• mein Ellbogen / tut / auch weh

Even after aber, German still starts a new main clause, so the conjugated verb stays in second position.

That is different from words like weil, which send the verb to the end:

• ..., weil mein Ellbogen auch wehtut.

aber means but, so it shows a contrast:

• The wound is small, but my elbow also hurts.

The contrast is that one problem seems minor, yet there is another pain as well.

If you used und, it would simply add information:

• Die Wunde an meinem Knie ist klein, und mein Ellbogen tut auch weh.

That is grammatically fine, but aber gives a clearer sense of contrast.

You can say both.

• der Ellbogen
• der Ellenbogen

Ellenbogen is very common and is often the dictionary form, but Ellbogen is also widely used in everyday German.

So this sentence is natural with Ellbogen, and you may also encounter:

• Mein Ellenbogen tut weh.

Both are correct.

Yes, that is also possible, but it is slightly different in focus.

• Die Wunde an meinem Knie = the wound on my knee
• Meine Wunde am Knie = my wound on my knee

The original sentence sounds a bit more neutral and descriptive.
Using meine makes it more personal or specific.

Also, am is a contraction of an dem, and here Knie would normally not use dem unless the phrasing changes quite a bit. So am Knie is common in some expressions, but in this exact sentence an meinem Knie is the more straightforward choice because it clearly means on my knee.

Yes, but the tone is a little different.

• Mein Ellbogen tut weh. = very common, everyday German
• Mein Ellbogen schmerzt. = correct, but a bit more formal or medical

For normal conversation, tut weh is often the most natural choice.

So learners should definitely know wehtun, because native speakers use it a lot for pain.