I know this won't help near term but I have 8 kids and when my older kids were young I had a doctor tell me that when they get colds and stuff to not give them over the counter meds. Those are designed for children with allergies and not for the common cold etc. If you give them these then their body doesn't learn to fight off sickness on it's own. Their bodies will slowly build up thier own immunity to these things and begin to fight it off itself. This made so much sense to me. I don't give my kids all those over the counter med. Only tylenol or motrin to help a headache, high fever or pain until I can see a doctor. My kids now don't get sick very often and if they do it goes quickly.
I know that doesn't help you now but maybe in the long run it will.
I have heard also about how valuable vitamin D is. I would definitely do that during the winter months.