Daktari aliniambia kwamba nikipiga chafya au nikianza kupata kikohozi darasani, nibaki nyumbani mpaka mafua yapungue.

It breaks down like this:

• a- = he/she
• -li- = past tense
• -ni- = me
• -ambia = tell / say to

So aliniambia means he/she told me.

In this sentence, the subject is Daktari, so the full idea is The doctor told me.

Kwamba means that and introduces a reported statement or instruction.

So:

• Daktari aliniambia kwamba... = The doctor told me that...

In everyday Swahili, people sometimes leave out kwamba, but it is very common and perfectly natural to use it.

Nikipiga contains the pattern ni-ki-:

• ni- = I
• -ki- = if / when
• -piga = hit / strike

So nikipiga literally means if/when I hit.

But here it is part of the expression kupiga chafya, which means to sneeze. So:

• nikipiga chafya = if I sneeze / if I happen to sneeze

This -ki- form is very common for if or when clauses.

This is just an idiomatic expression. Swahili often uses a general verb plus a noun, where English uses one verb.

So:

• kupiga chafya = to sneeze
• literally, something like to hit a sneeze

You should learn it as a set phrase. A lot of everyday Swahili works this way.

This part means if I start getting a cough.

Breakdown:

• ni- = I
• -ki- = if / when
• anza = begin / start
• kupata = to get
• kikohozi = cough

So:

• nikianza = if I start
• nikianza kupata kikohozi = if I start getting a cough

Using kuanza kupata gives the idea that the cough is beginning or developing, not just that it already exists.

They refer to different symptoms or illnesses:

• chafya = a sneeze / sneezing
• kikohozi = a cough
• mafua = a cold or sometimes flu-like cold symptoms, especially a runny nose/cold

So the sentence moves from symptoms in class to staying home until the cold improves.

Darasani means in the classroom or in class.

It comes from:

• darasa = class / classroom
• -ni = a locative ending, often meaning in / at / to

So:

• darasa = classroom
• darasani = in the classroom

This -ni ending is very common in location words.

Nibaki is a subjunctive form. Here it expresses what the doctor told the speaker to do: that I should stay or that I stay at home.

Breakdown:

• ni- = I
• -baki = remain / stay

In this kind of reported instruction, Swahili often uses the subjunctive:

• aliniambia nibaki nyumbani = he/she told me to stay home

So nibaki is not a plain present tense. It shows instruction, intention, or what ought to happen.

Yapungue is also a subjunctive form, and it means they lessen or they reduce.

Breakdown:

• ya- = subject agreement for mafua
• -pungue = lessen / decrease

So:

• mpaka mafua yapungue = until the cold symptoms lessen

After mpaka meaning until, Swahili often uses this kind of form when talking about a future result or endpoint.

Because mafua belongs to noun class 6, and class 6 usually takes agreement with ya-.

So:

• mafua yapungue
• not mafua ipungue or mafua apungue

This is a noun-class agreement issue. Even though mafua is often translated as a cold, grammatically it behaves like a class 6 noun.

In meaning, it usually refers to the illness a cold or cold symptoms, even though its form looks plural from an English point of view.

So you should not think of it as literally colds here. It is just the normal Swahili word used for a cold / cold symptoms.

That is why the translation can be singular in English even though the grammar follows class 6 agreement in Swahili.

Here mpaka means until.

So:

• nibaki nyumbani mpaka mafua yapungue = I should stay home until the cold gets better / until the symptoms lessen

In other contexts, mpaka can also mean things like up to, as far as, or even, but here until is the correct sense.

Yes. The sentence has three main parts:

1. Daktari aliniambia kwamba...
   = The doctor told me that...

2. nikipiga chafya au nikianza kupata kikohozi darasani
   = if I sneeze or start getting a cough in class

3. nibaki nyumbani mpaka mafua yapungue
   = I should stay home until the cold symptoms lessen

A very literal structure would be something like:

• The doctor told me that if I sneeze or if I start getting a cough in class, I should stay home until the cold lessens.

So it is basically: reporting verb + kwamba-clause + condition + instruction/result.