Meine linke Hand tut weh.

Because Hand is a feminine noun: die Hand.

The possessive word mein- changes its ending to match the noun’s gender, number, and case. With a feminine singular noun in the nominative, it becomes meine.

So:

• mein Arm = my arm
• meine Hand = my hand

Also, because meine already works like a determiner, you do not add die before Hand.

That is the adjective ending.

In meine linke Hand, linke describes Hand, so it has to take an ending. Because meine already shows feminine singular nominative, the adjective takes the weak ending -e.

So the pattern is:

• meine linke Hand
• deine rechte Hand
• die kalte Suppe

This is a very common pattern in German adjective declension.

It is in the nominative case because it is the grammatical subject of the sentence.

In this sentence, Hand is the thing that tut weh. So German treats meine linke Hand as the subject.

That is why you get:

• Meine linke Hand tut weh.

not a dative or accusative form here.

Tut is the 3rd person singular present tense form of tun.

Here it is being used as part of the verb wehtun.

So:

• infinitive: wehtun
• present tense: ich tue weh is not normally used this way for body pain, but
  es tut weh, meine Hand tut weh, die Augen tun weh

Because Hand is singular, the verb is singular too:

• die Hand tut weh
• die Hände tun weh

Because wehtun is a separable verb.

In a normal main clause, separable verbs split:

• Meine linke Hand tut weh.

Here:

• tut = the conjugated verb part
• weh = the separated prefix-like part at the end

In the infinitive or in some other structures, it stays together:

• Meine linke Hand kann wehtun.
• Ich weiß, dass meine linke Hand wehtut.

So the split is completely normal German word order.

Yes — it is best to learn wehtun as a single expression meaning to hurt.

Literally, it does not map neatly onto natural English word-for-word. Even though tun by itself often means to do, in wehtun the whole expression functions like one verb.

So learn these as fixed patterns:

• Das tut weh.
• Mein Rücken tut weh.
• Die Füße tun weh.

That will sound much more natural than trying to interpret each part separately every time.

German very often includes a dative pronoun with body-part pain:

• Die linke Hand tut mir weh.
• Mir tut die linke Hand weh.

But in Meine linke Hand tut weh, the owner is already clear from meine, so mir can be left out.

Both are natural. The version with mir can sound a little more personal or explicit about who is feeling the pain.

It is definitely natural, but there are other common ways too.

Very common everyday alternatives:

• Mir tut die linke Hand weh.
• Die linke Hand tut mir weh.

A bit more formal or clinical:

• Meine linke Hand schmerzt.
• Ich habe Schmerzen in der linken Hand.

So Meine linke Hand tut weh is simple, correct, and natural, especially for a learner.

A rough English-friendly version is:

MY-nuh LIN-kuh hant toot vay

A more accurate pronunciation is roughly:

• meine → MY-nuh
• linke → LING-kuh
• Hand → hahnt
• tut → toot
• weh → vay

A few useful pronunciation notes:

• w in German sounds like English v
• h in Hand is pronounced
• eh in weh is a long ay sound
• d at the end of Hand is pronounced more like t

So weh sounds like vay, not like English way.