Can building work make my children sick?

[thinkingpositive]

Hello...
I wonder if you knowledgeable people may be able to shed some light?
We are building an extension on our property and we are 9 weeks (but only realistically 6 weeks) into our build. We have no kitchen and using a make shift one with no hot water or heating ( besides a little gas heater). Yes it's getting very cold.
3 adults, 2 children are sharing 2 bedrooms and a lounge.
My question is, can the building work effect the health of my 2 boys ( under 4)?
My mum had pneumonia, now the boys both have tonsillitis and it's taking forever to get better.
I'm wondering if it has anything to do with the build?

Building works combined with the rough conditions you are living in may impact on the health.
No heating will make the house damp and cold, no kitchen means you may rely more on packaged food vs fresh.
When you removed the walls did you find mould? Do you properly protect the doors with plastic sheets to avoid the dust?
Can't you go and live somewhere else for a while?

Due to new sleeping arrangements they might not be getting much sleep or having disturbed sleep. That can cause you to feel run down. No heating means your body works harder at keeping warm too.

Can you find them somewhere to stay for a fee days? Or get another heater, give them a bath and some thermal underwear under their pjs