Nach dem Sturz tut mir der Ellbogen weh, aber die Wunde ist nicht tief.

Because nach takes the dative case when it means after in a time sense.

• der Sturz = the fall (nominative)
• dative singular of der Sturz = dem Sturz

So:

• nach dem Sturz = after the fall

This is a very common pattern:

• nach dem Essen = after the meal / after eating
• nach der Arbeit = after work
• nach dem Unfall = after the accident

weh tun is a very common German expression meaning to hurt.

In this sentence:

• Der Ellbogen tut mir weh. = My elbow hurts / The elbow hurts me

The expression is built like this:

• [body part / thing] + tut + [person in dative] + weh

Examples:

• Der Kopf tut mir weh. = My head hurts.
• Die Beine tun mir weh. = My legs hurt.
• Tut dir der Rücken weh? = Does your back hurt?

Notice that weh goes to the end of the clause in a normal main clause because tun is the conjugated verb and weh belongs with it as part of the expression.

Because the person who feels the pain is in the dative case with weh tun.

So German says, literally:

• The elbow hurts to me

That is why you get:

• mir = to me
• dir = to you
• ihm/ihr = to him/her
• uns = to us

Examples:

• Der Zahn tut mir weh. = My tooth hurts.
• Tut dir der Fuß weh? = Does your foot hurt?
• Die Schulter tut ihm weh. = His shoulder hurts.

Using mich would be wrong here.

Because der Ellbogen is the subject of the verb tut.

In Der Ellbogen tut mir weh:

• der Ellbogen = subject
• tut = verb
• mir = dative object
• weh = part of the expression weh tun

Even though English says my elbow hurts, German often uses the body part itself as the subject:

• Der Ellbogen tut mir weh.
• literally: The elbow hurts me

So the nominative form der Ellbogen is correct.

German often uses the definite article with body parts when it is already clear whose body part is meant.

So instead of saying:

• mein Ellbogen

German very naturally says:

• der Ellbogen

because mir already tells us whose elbow it is.

This is very common with body parts:

• Ich wasche mir die Hände. = I wash my hands.
• Er hat sich den Arm gebrochen. = He broke his arm.
• Der Kopf tut mir weh. = My head hurts.

Using mein Ellbogen is not impossible, but it is less natural here.

Because in a German main clause, the conjugated verb goes in second position, and the rest of the verbal expression often goes later.

With weh tun:

• tut is the conjugated verb
• weh stays later in the clause

So:

• Der Ellbogen tut mir weh.

This is similar to separable-verb behavior, and learners often find it helpful to think of weh tun as a fixed expression whose parts split in main clauses.

Compare:

• Mein Rücken tut weh.
• Warum tut dein Knie weh?

The phrase Nach dem Sturz comes first, so the conjugated verb must come immediately after it because German main clauses follow the verb-second rule.

Structure:

• Nach dem Sturz = time expression
• tut = conjugated verb in second position
• mir = dative object
• der Ellbogen = subject
• weh = part of weh tun

So even though der Ellbogen is the subject, it does not have to come first.

You could also say:

• Der Ellbogen tut mir nach dem Sturz weh.

That is grammatical, but the original version emphasizes after the fall more strongly.

Because aber connects two main clauses, and in German those are normally separated by a comma.

The two clauses are:

1. Nach dem Sturz tut mir der Ellbogen weh
2. aber die Wunde ist nicht tief

So the comma is required.

This is very common with conjunctions like:

• aber = but
• und = and
• oder = or

Especially when full clauses are being linked, the comma helps show the structure clearly.

die Wunde means the wound, and tief means deep.

German commonly describes wounds as deep or not deep, just like English:

• Die Wunde ist tief. = The wound is deep.
• Die Wunde ist nicht tief. = The wound is not deep.

Grammatically:

• die Wunde = subject
• ist = is
• nicht tief = not deep

This is a simple subject + sein + adjective structure.

Yes. You could say:

• Nach dem Sturz schmerzt mir der Ellbogen.
• or more naturally: Nach dem Sturz schmerzt mein Ellbogen.

But weh tun is usually more common and more conversational in everyday German.

Compare:

• Der Ellbogen tut mir weh. = very common, everyday
• Mein Ellbogen schmerzt. = also correct, slightly more formal or descriptive

For learners, weh tun is the more useful everyday pattern to master first.

Ellbogen is standard and very common. You may also sometimes see Ellenbogen, which is also accepted and very common in modern German.

So both exist:

• der Ellbogen
• der Ellenbogen

In everyday use, many speakers prefer Ellenbogen, but Ellbogen is not wrong.