The best thing to do if Sam gets a cold is to keep him warm and within reach, in case he takes a turn for the worse. Dean will keep him drinking plenty of liquids, and order some chicken noodle soup. Medicine they’ll only ever attempt if they’re desperate, since they aren’t sure how it’ll react with his system.
The hardest part with Dean is convincing him to relax and take it easy long enough to get better, and Sam is the master at talking Dean into things. Some puppy eyes, or pretending he’s sick as well if it comes down to it. There’s no way Dean can go on hunting if Sam’s sick, so clearly he has to get Sam some chicken noodle soup, and he can’t just leave it since it would all go to waste, so he’ll just take some soup for himself and then fall asleep on the bed watching Dr. Sexy, MD, and Sam will smile proudly at himself for working his magic yet again.