I haven't had any problems vaping while sick. I have heard some say that vaping hurt when they were sick, my wife was one of them. You may want to keep your mouth piece or drip tip cleaned more often though so you don't reinfect yourself.
I have a Mark's mod and a homade one of my own. I have to admit, Mark's is my favorite and the best part is they were both free for me! Thanks again Mark!