I'm a total wuss about it myself.

Years ago I got myself into trouble because I wouldn't stop riding despite a sinus infection. It wound up lasting for 11 weeks, I was miserably sick the whole time (although it never did go into bronchitis the way they usually do with me), and I finally had to take a whole week off work - not just riding - so i could recover.

Exercise does depress the immune system. I might go for a walk outside, but my rule is when I'm sick, I don't want to break a sweat. YMMV. Hope you feel better soon.