האף שלי סתום, ולכן אני לא יכולה לישון טוב.

Because Hebrew often uses the definite article ה־ with a possessed noun when you mean a specific thing, like my nose.

So:

• האף שלי = my nose / the nose of mine
• אף שלי would sound less natural here

With body parts, the definite form is especially common, because you are usually talking about one specific, known thing.

Here, האף is pronounced roughly ha-af.

• אף = nose
• האף = the nose

A learner may also notice that אף can mean something else in other contexts, like even or also not in more formal/literary Hebrew. But in this sentence, because of the context and the definite article ה־, it clearly means nose.

סתום literally means closed, shut, or blocked.

In this sentence, האף שלי סתום means my nose is blocked/stuffed up. This is a very natural way in Hebrew to talk about nasal congestion.

So although the literal sense is closed, the natural English meaning is my nose is stuffed up or my nose is blocked.

Because סתום has to agree with האף in gender and number.

• אף is masculine singular
• so the adjective must also be masculine singular: סתום

If the noun were feminine singular, you would use סתומה.

This is basic adjective agreement in Hebrew.

Because the speaker is female.

In Hebrew, words like יכול / יכולה agree with the subject:

• אני לא יכול = I can't said by a male
• אני לא יכולה = I can't said by a female

So this sentence is specifically being said by a woman or girl.

Because אני לא יכולה לישון means I cannot sleep or I’m unable to sleep, not simply I’m not sleeping.

Compare:

• אני לא ישנה = I’m not sleeping / I do not sleep (female speaker)
• אני לא יכולה לישון = I can’t sleep

The sentence is talking about inability, so יכולה is the right choice.

After יכול / יכולה (can / be able to), Hebrew normally uses an infinitive.

So:

• יכולה לישון = can sleep
• לא יכולה לישון = cannot sleep

The ל־ is the normal marker for the infinitive in Hebrew, similar to English to in to sleep.

• לישון = to sleep

ולכן means and therefore, and so, or simply so.

It is made of:

• ו־ = and
• לכן = therefore / so

So the sentence structure is:

• האף שלי סתום = My nose is blocked
• ולכן אני לא יכולה לישון טוב = and therefore I can’t sleep well

It is a perfectly natural connector, though slightly more formal than a very casual אז in some contexts.

Yes, טוב literally means good, but in everyday Hebrew it is very common to use טוב where English would use the adverb well.

So:

• לישון טוב = to sleep well

A more formal adverb is היטב, and you may also hear:

• לישון היטב = to sleep well

But in normal spoken Hebrew, טוב is extremely common and natural.

No. It is just one natural option.

Other common ways to express the same basic idea would be:

• האף שלי סתום, אז אני לא יכולה לישון טוב.
  My nose is blocked, so I can’t sleep well.

• אני לא יכולה לישון טוב כי האף שלי סתום.
  I can’t sleep well because my nose is blocked.

• בגלל שהאף שלי סתום, אני לא יכולה לישון טוב.
  Because my nose is blocked, I can’t sleep well.

So ולכן is natural, but not the only choice.

Yes, it is natural and standard here.

The comma separates two clauses:

• האף שלי סתום
• ולכן אני לא יכולה לישון טוב

In English, this works similarly to writing My nose is blocked, so I can’t sleep well.

In casual writing, punctuation may vary, but the comma here is normal and helpful.