Well, I'll tell you a little story:
Last year, I was really sick and called in sick to work. Mid-day, I puked and emptied my bowels, and felt a million times better---you always feel better after that. It wasn't worth going into work, so I thought I'd get some housework done (I was in the middle of plumbing our half-bath). Now, this was a pretty big commitment, because it meant unhooking some pipes and having to shut off the main water valve to the house...and since there was no intermediate shutoff valve, we wouldn't have any water until I finished the job. SO I get into it, and I come upon a pipe that's been in the same position for the last 50 years, and it might as well be welded together. I'm screwed. And I'm also feeling worse. The initial period of wellness following the aforementioned expulsions was wearing off. But here I am, downstairs, on a stepladder, with two heavy pipe wrenches held above my head, and my physical condition getting worse and worse. I put all my strength (and I'm a strong guy) into it, but they would not budge. I'd have to try and try for a few minutes, then I'd start feeling so terrible that I'd drop from the ladder and curl up in the fetal position for a few minutes waiting for it to subside. I couldn't give up and go back to bed, because our whole house was water-less until I finished. It was awful, but I finally got it off and finished the plumbing job later that night. But the hours spent writhing in pain and trying to wrestle 50 year old galvanized iron pipes were some of the worst hours of my life.
The moral of the story here is, unless you're 100% sure that you won't start feeling bad again in a couple hours, I would say don't try it. Like with my plumbing job, once you get started, you have to finish. So Just be sure that you are "done" with being sick, because the last thing you want is to get wretchedly ill right in the middle of the mash or the boil.
As for contaminating your brew, I doubt whatever you have infecting your body is the kind of bacteria that will infect a beer. Most of that stuff lives on your skin all the time anyway.
And as for the ethical implications, if you took a day, you took a day. It's a "personal day", and you can use it as you see fit. If you spent the morning of your personal day being sick, and the afternoon brewing, it makes no difference to your employer, or shouldn't.
