I've had similar dreams but I've never gotten sick from then.
It could just be lack of a good nights sleep. You can be sleeping but if you're tossing and turning because of bad dreams then you're body and mind isn't getting the rest it needs. Lack of rest can result in lost of appetite too and the lack of rest and nutrition can weaken the immune system.
Just a thought, you might try something to help you sleep. Chamomile tea is suppose to help but I can't be certain, or don't eat certain types of food before you go to bed.