Hi LucidBlue...I don't think a human can catch like a stomach or URI from a cat. I think it might be physically impossible or rather the minute amounts of virus or bacteria that a cat might have can be almost instantaneously killed by humans on contact. But there are a few things to consider. One is, when you clean out her litter box, do you wash your hands immediately afterwards? Have you been disinfecting her box so germs don't spread around? If you have a URI and your cat has had one, maybe there is a mold problem or dust problem in your house that may have caused it for either one of you? Or maybe she ate something bad that you might have cooked as a "present" and you ate it too? I don't know! So many possibilities but I don't think that you can catch what you cat has. I am by far NOT an expert, so are there any out there???
Oh and another thing I thought of...could your kitty being sick cause stress on your immune system and then it manifests as something else for you? That could be coincidental. My cat has a little virus thing a few weeks back and I was so worried for her that I ended up getting...well, let's just put it this way, I was on the terlet for a loooooong time!
Good luck and hope you and your kitty are doing better