Hi mum, I feel you, this stage with playgroup is really like cycle after cycle of cough and runny nose, quite draining for both child and parents. I went through the same also and honestly there’s no fast “home cure”, it’s more about supporting the body while it clears on its own. What helped me was lots of fluids, saline spray for blocked nose, steamy bathroom before sleep, and honey only if child is above 1 year old. I also realised reducing exposure where possible (like good hand hygiene and changing clothes after school) helped a bit. If it keeps happening very frequently or cough is very persistent, I would still check with PD to rule out asthma or allergy tendency.
Honey warm water is a good start, my friend's daughter had the same issue and she also added a small slice of ginger to the warm honey drink and found it helped soothe the throat quite a bit. Might also be worth mentioning to your PD how frequently she's falling sick, just to rule out anything else going on.