yeah it happens to me but I think for other reasons. I usually start playing basketball more, like this past week where I played saturday sunday then twice on monday. Combine that with walking around half the day monday with a sweaty shirt(i sweat at an incredible rate~ 5+lbs an hour), and tons of people coughing on me I knew I was pretty much asking for it, but I kept telling myself I'll stop later.
I have tried to lose weight without getting sick. Usually if I just try to ease into it instead of going all out with a ton of cardio, and cutting half the food I won't get sick. But it's hard to motivate myself to ease into something.
Protein creatine and bcaa's aren't really immune boosting foods. Vitamin C is good but if your on a healthy diet you should be getting enough.. OJ, Strawberries, Brocolli damn near everything has it. Try some vitamins with zinc, vitamin D, magnesium and calcium, and either cycle the carbs or cut them slowly.