There are certain people meds that are fine for cats, depending on their weight and size. However, I'd forego the baby aspirin. Go buy some "Little Noses" pediatric saline nose drops. Try putting a couple drops in each nostril. You can also bring the baby in the bathroom and close the door. Turn on the hot water in the shower and let the steam build up. This will help break up the congestion. Wash his eyes with a warm moist washcloth to clear out all the gunk. This will at least help till you can get him to the vet.

Get a bin or box and put either a hot water bottle or heating pad (on low) and cover it with a small towel. Put the baby in the box and cover the box lightly with a small blanket.

Good luck and keep us posted!!