I don't keep DS off with a cold as that's an occupational hazard of childcare.

But chest infection/flu (he'll be acting "ill" usually then but do go to the doctor if you keep him off nursery as if he's too ill to go to nursery he needs a check-over) DS would be off. As he would for anything that created spots. Vomiting and diarrhoea is a no-go too.

HTH and hope the GP finds nothing wrong aside from a cold and cough.