Kiam mia gorĝo doloras, mi prenas la medikamenton kun akvo.

Kiam means when. It introduces a time clause:

• Kiam mia gorĝo doloras = When my throat hurts

This works much like English. In Esperanto, a clause with kiam often comes before the main clause, but it could also come after it:

• Mi prenas la medikamenton kun akvo, kiam mia gorĝo doloras.

Both are understandable.

Because mia gorĝo is the subject of doloras.

In the clause:

• mia gorĝo doloras

the throat is the thing that hurts, so it is the subject, not the direct object. Subjects do not take -n.

Compare:

• Mia gorĝo doloras. = My throat hurts.
• Mi tuŝas mian gorĝon. = I touch my throat.

In the second sentence, mian gorĝon gets -n because it is the direct object of tuŝas.

Esperanto often uses the present tense in general statements or habitual situations, just like English can:

• Kiam mia gorĝo doloras, mi prenas la medikamenton kun akvo.

This can mean something like:

• When my throat hurts, I take the medicine with water.

It describes what the speaker does in that situation, not necessarily only one specific moment.

Yes. Dolori means to hurt, to ache, or to be painful.

So:

• Mia gorĝo doloras literally means something like My throat hurts or My throat is painful.

This is a very common Esperanto pattern:

• Mia kapo doloras. = My head hurts.
• Mia dorso doloras. = My back hurts.

The -n marks the direct object.

In:

• mi prenas la medikamenton

the thing being taken is the medicine, so medikamento becomes medikamenton.

Also notice that both the article and noun stay together as one noun phrase:

• la medikamento = the medicine
• la medikamenton = the medicine as a direct object

Only the noun gets -n, not la.

Yes, both can be possible, depending on meaning.

• la medikamenton = the medicine
  This suggests a specific medicine, one already known or understood from context.
• medikamenton = medicine / a medicine

So the sentence with la sounds more like the speaker has a particular medicine in mind.

Because Esperanto often leaves out la when talking about a substance in a general way.

• kun akvo = with water

This means water as the drink used to take the medicine, not some specifically identified water.

If you said kun la akvo, it would usually mean with the water—some specific water already known in the conversation.

It can cover both, depending on context.

Esperanto present tense -as is flexible:

• mi prenas can mean I take
• or I am taking

In this sentence, the natural meaning is the habitual one:

• When my throat hurts, I take the medicine with water.

Not with the same meaning.

• preni medikamenton = to take medicine
• trinki akvon = to drink water

In the sentence, the speaker is taking the medicine, and they do it with water. So prenas is the right verb.

If you used trinkas, it would sound like the medicine itself is being drunk, which is possible only if the medicine is liquid.

Gorĝo means throat.

The letter ĝ is pronounced like the j in jam or judge.

So gorĝo sounds approximately like GOR-jo, with the first g as a normal hard g, and the ĝ as the English j sound.

Esperanto often allows word order similar to English, especially in simple sentences, so this sentence feels familiar:

• Kiam mia gorĝo doloras, mi prenas la medikamenton kun akvo.

But Esperanto is generally more flexible than English because of endings like -n. Those endings help show grammatical roles even if the order changes.

Still, the most natural order for learners is usually the straightforward one used here.

Yes. That is possible.

• Kiam mia gorĝo doloras
• Kiam doloras mia gorĝo

Both mean the same thing. The first version is probably more straightforward for learners, while the second may sound a little more stylistic or emphatic depending on context.

Yes, medikamento is a normal Esperanto word for medicine or medication.

Depending on context, you might also see more specific words, but medikamento is a good general-purpose word and fits this sentence well.