Coughing at night; 3 year old.

My just turned 3 year old has a viral infection. First 2 days he had a fever, was very hot to touch. Then had a mucus chesty cough with a runny & blocked nose for around 8 days. As well he just was not himself, very sluggish, not eating, tired all the time & very cuddly (which is not him, he hates cuddles unless it is bedtime). We are 2 weeks & 4 days in now. He still has a runny nose, not too bad, as in I am not cleaning it up 10+ times a day, only 2 or 3 now. And he still coughs at night, he does during the day but only when he has been active, jumping on the bed, running round etc. The bad coughs are at night. He coughs all night long. He occasionally has a mucus cough and I have to sit him up but they are mostly dry chesty coughs. He seems fine during the day it is just nighttime. Is this normal after a viral infection? I am going to call the doctors to try get an appointment but they are such a pain to get into at the moment 😔 They never want to see anyone.

Should I be asking them to look into asthma? Or is he getting over the end of it?

Also he has tested negative for Covid 4 times now.