It could be a bit of a suppression of the immune system, people regularly get colds after running a marathon. I would think exercise induced asthma would clear well before a few days. If you are concerned about EIA, you might want to check with your doctor. There are ways to treat it that will leave most people who suffer this able to manage it pretty well.
As for what to eat after the race, just think healthy foods. Fruits are very good for boosting vitamins and will replace some of the carbs you burned. Bread products like bagels are also good. Personally, I love having a bagel with peanut butter on it and a banana on the side, though the peanut butter can be a challenge at a race. Also, don't forget the fluids. Drink plenty of water as soon as possible afterward.