Dün çenemi kapıya çarptım, bugün hâlâ biraz ağrıyor.

Because çenemi means my chin as a specific object.

It breaks down like this:

• çene = chin
• çenem = my chin
• çenemi = my chin (as the definite direct object)

So in çenemi kapıya çarptım, the speaker is saying I hit my chin against the door.

Turkish very often uses possessive endings with body parts where English might simply use my.

çenemi = çene + m + i

• çene = chin
• -m = my
• -i = accusative case marker

So:

• çenem = my chin
• çenemi = my chin as the thing affected by the action

The accusative appears because the chin is a definite, specific object being hit.

Because with çarpmak, the thing you hit against / into often takes the dative.

• kapı = door
• kapıya = to the door / against the door

So:

• çenemi kapıya çarptım = I hit my chin against the door

This is a very common Turkish pattern:

• duvara çarpmak = to hit/crash into the wall
• masaya çarpmak = to bump into the table

So even though English says hit X on/against Y, Turkish uses the direct object for the thing hit and dative for what it hit against.

çarptım is the 1st person singular definite past form of çarpmak.

Breakdown:

• çarpmak = to hit, strike, bump into
• stem: çarp-
• past tense: -tı / -ti / -tu / -tü (chosen by vowel harmony and consonant voicing rules)
• -m = I

So:

• çarptım = I hit / I bumped

In this sentence, Dün already tells you it happened yesterday, and çarptım confirms it as a completed past action.

Here çarpmak means something like:

• to hit
• to bump
• to knock against

So çenemi kapıya çarptım means I hit/bumped my chin against the door.

Depending on context, çarpmak can also be used for things like:

• a car crashing into something
• accidentally knocking a body part against something
• striking something

So it is a very useful verb for collisions and impacts.

Yes, and it is very close in meaning.

Compare:

• Çenemi kapıya çarptım.
  = I hit my chin against the door.

• Çenem kapıya çarptı.
  = My chin hit the door.

The first version focuses more on my action as the speaker.
The second version presents the chin as the grammatical subject.

Both are natural, but çenemi kapıya çarptım is especially common when talking about accidentally hitting part of your body.

The subject is understood from context: it is çenem or simply it referring to the chin.

Turkish often omits words that are obvious.

So the full idea is:

• Bugün hâlâ biraz ağrıyor.
• literally: Today, it still hurts a little.

If you wanted to make it explicit, you could say:

• Bugün çenem hâlâ biraz ağrıyor.
• Today my chin still hurts a little.

But leaving it out sounds natural because the listener already knows what is being talked about.

Ağrıyor comes from ağrımak, which means to ache / to hurt.

With body parts, it is very commonly used for pain:

• Başım ağrıyor. = My head hurts.
• Dişim ağrıyor. = My tooth hurts.
• Çenem ağrıyor. = My chin hurts.

In English, hurts is often the best translation, but aches can also fit depending on context.

Biraz means a little / somewhat.

So:

• hâlâ ağrıyor = it still hurts
• hâlâ biraz ağrıyor = it still hurts a little

It softens the statement and makes the pain sound mild or moderate rather than severe.

Hâlâ means still.

So:

• bugün hâlâ biraz ağrıyor = today it still hurts a little

About the spelling:

• hâlâ = still
• hala = paternal aunt

In careful standard spelling, the circumflex helps distinguish the two. In casual typing, many native speakers leave it out, but hâlâ is the standard spelling for still.

The sentence is quite natural and straightforward.

• Dün = yesterday
• çenemi = my chin
• kapıya = against/to the door
• çarptım = I hit
• bugün = today
• hâlâ = still
• biraz = a little
• ağrıyor = hurts

A very literal ordering would be:

• Yesterday my chin against-the-door I-hit, today still a little hurts.

Turkish word order is flexible, but placing the verb near the end is the normal pattern. Time expressions like dün and bugün often come near the beginning of their clauses.

The comma joins two closely connected clauses:

• Dün çenemi kapıya çarptım,
• bugün hâlâ biraz ağrıyor.

This is natural because the second clause is the result of the first.

You could also say:

• Dün çenemi kapıya çarptım ve bugün hâlâ biraz ağrıyor.

But the version with the comma sounds more natural and less heavy.
You could also split it into two sentences:

• Dün çenemi kapıya çarptım. Bugün hâlâ biraz ağrıyor.

All of these work.

In ağrıyor, the ğ is not pronounced like a strong consonant in the way English speakers might expect.

Very roughly:

• ağrıyor sounds something like aa-rı-yor or a-rı-yor, with a lengthening/smoothing effect

The exact sound depends a bit on accent and speed, but the key point is:

• ğ usually does not sound like a hard g
• it often lengthens the preceding vowel or creates a glide

So don't try to pronounce it like an English g in go.