Η πληγή στο χέρι της είναι μικρή, αλλά το δάχτυλο είναι ακόμα πρησμένο.

Because πληγή is a feminine noun in Greek. Greek nouns have grammatical gender, and the article has to match the noun:

• η πληγή = the wound
• not το πληγή

You can also see the feminine gender later in the adjective:

• η πληγή ... είναι μικρή
• μικρή is the feminine form of small

So both the article η and the adjective μικρή agree with πληγή.

Adjectives in Greek must agree with the noun they describe in gender, number, and case.

Here, πληγή is:

• feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• masculine: μικρός
• feminine: μικρή
• neuter: μικρό

That is why the sentence says:

• Η πληγή ... είναι μικρή

Literally, στο χέρι της means in/on her hand.

It breaks down like this:

• σε = in / on / at
• το = the
• στο = contraction of σε + το
• χέρι = hand
• της = her

So:

• στο χέρι της = on her hand / in her hand / on her arm, depending on context

In this sentence, English would naturally say the wound on her hand.

In Greek, possession is often shown with a weak genitive pronoun placed after the noun.

So:

• το χέρι της = her hand
  literally: the hand of her

This is a very common Greek pattern:

• το σπίτι μου = my house
• η μητέρα του = his mother
• το βιβλίο μας = our book

So Greek usually does noun + possessive pronoun, not her hand in the English order.

της here is in the genitive case and means her.

Greek often uses the genitive for possession. So in:

• το χέρι της

the word της is a genitive pronoun meaning of her.

Be careful: της can also mean to her in other contexts, so the exact meaning depends on the sentence. Here, because it follows a noun, it clearly shows possession:

• το χέρι της = her hand

Because δάχτυλο is a neuter noun.

So it takes:

• the neuter article το
• the neuter adjective form πρησμένο

That is why the sentence says:

• το δάχτυλο είναι ακόμα πρησμένο

Greek noun gender is something you usually have to learn together with the noun itself:

• η πληγή = feminine
• το χέρι = neuter
• το δάχτυλο = neuter

πρησμένο is the neuter singular form of the adjective swollen.

It agrees with το δάχτυλο, which is neuter singular.

The adjective forms are:

• masculine: πρησμένος
• feminine: πρησμένη
• neuter: πρησμένο

So:

• το δάχτυλο είναι πρησμένο = the finger is swollen

Greek often uses είναι + adjective where English also uses is + adjective.

Here ακόμα means still.

So:

• είναι ακόμα πρησμένο = it is still swollen

Depending on context, ακόμα can also mean even or yet, but here still is the natural meaning.

Examples:

• Είναι ακόμα εδώ. = He/She is still here.
• Δεν έχω φάει ακόμα. = I haven’t eaten yet.

αλλά means but.

It connects two contrasting ideas:

• Η πληγή ... είναι μικρή = The wound is small
• αλλά το δάχτυλο είναι ακόμα πρησμένο = but the finger is still swollen

So the contrast is:

• the wound itself is not serious in size,
• but the finger is still swollen.

Greek often repeats the verb to be in each clause, just as English often does.

The sentence has two coordinated parts:

1. Η πληγή στο χέρι της είναι μικρή
2. αλλά το δάχτυλο είναι ακόμα πρησμένο

Each part has its own subject and predicate, so είναι appears in both.

You could think of it as:

• The wound ... is small
• but the finger is still swollen

χέρι can mean hand and can also sometimes cover arm in broader usage, depending on context.

In this sentence, because it later mentions δάχτυλο (finger), the natural interpretation is hand:

• Η πληγή στο χέρι της = The wound on her hand

So even if χέρι can be somewhat broader in other contexts, here hand is the best translation.

Greek uses the definite article very frequently, often more often than English.

Here it is completely normal to say:

• η πληγή = the wound
• το δάχτυλο = the finger

Even when English might sometimes omit an article in other contexts, Greek often keeps it. In this sentence, both nouns are specific and known in context, so the articles are expected.

Yes, but the meaning would change.

• το δάχτυλο = the finger
  a specific finger, understood from context
• ένα δάχτυλο = a finger
  one finger, less specific

In your sentence, το δάχτυλο sounds natural because it refers to the affected finger already understood as part of the injured hand.

Not exactly, though they are related.

• πληγή usually means wound
• τραύμα can mean injury, trauma, or wound in a broader sense

In this sentence, πληγή is a good choice because it refers to a wound on the hand. τραύμα would sound broader or more medical/general depending on context.

A more literal version would be:

• The wound on the hand of hers is small, but the finger is still swollen.

That is not natural English, but it helps show the Greek structure:

• Η πληγή = the wound
• στο χέρι της = on her hand
• είναι μικρή = is small
• αλλά = but
• το δάχτυλο = the finger
• είναι ακόμα πρησμένο = is still swollen

So the natural English version is:

• The wound on her hand is small, but the finger is still swollen.