My son had a similar problem when getting his tonsills out. The surgeon said exactly the same thing, it really is the anaethetists call on the day of the surgery.

He had no temp and his chest was clear and his surgery went ahead no worries. He even had a cough but the decision was made that it was more important to get the tonsills out rather than risk another bout.

HTH
Spring x

ETA: Just be careful what you get from the chemist, it is important for your surgeon and anaethetists to know what you are taking even if it is just over the counter. I'd be inclined just to keep up fluids and rest. The other thing is some surgeons advise not having nurophen or blood thinning drugs before surgery. Might be best just to stick with chicken soup and a rest.