Should I feel bad for being sick and not going to work, even though I knew we were already short staffed?

I work as a Chiropractic Assistant, doing massage and dealing closely with people and I've come down with a flu. Its relativity mild, I'm not vomiting or having diarrhea, though I feel like I should. I have chills, aches, nausea, I can't eat, and a painful headache. I already knew my co worker wouldn't be in, but I just don't think I could lean over others all day. The office is really tight-knit and we all love each other and yet I feel very guilty, like I'm loading them with my problems. Maybe I'm just looking for some reassurance that I did the right thing of not going in, even though I put others in a hard position.