OCD?

So there's a new girl here at work.  She's only here twice a week for 10 hours total.  For the most part, I like new girl.  Except for a few things...

Since she started in October, I don't believe she's ever not been sick.  She has three young kids - I blame them.

She never covers her mouth when she coughs, which is all the damn time.

She doesn't wash her hands after using the bathroom (eew!  and don't ask how I know this.)

Now I don't consider myself to be some kind of Jack Nicholson when it comes to germs and neatness, but these things really freak me out.  It takes all I have in me not to yell "COVER YOUR MOUTH!!" every time I hear her cough.  I also need to buy stock in Airborne™ because I've been taking it like candy to try and not be infected by her.

Am I alone in being grossed out by these things?  Do I have some kind of low-level OCD?