I'm the same way but not so much with pee, if you know what I'm saying. I have OCD and have a problem with people who are not modest about taking a crap. I had a roommate once whose boyfriend would ruthlessly punish the toilet in our apartment every time he came over. He would regale us with vocal interpretations of how well his bowels were functioning. If I'm in a restaurant I get incensed if expected to sit near the restrooms. I can't even remember the last time I sat down on a public toilet. I don't like to pee in them either, but I do. I usually flush the urinal first and stand waaaaay back to avoid splashback. For me, it's about modesty. Not sure if that's the right word. I just don't want people to think I'm as disgustingly demonstrative with their bodily functions as I think they can be.
AS for your problem, have you thought about adult diapers? I'm not making fun or trying to be cheeky.

You don't have to use them constantly, but in certain situations they can be a lifesaver for you, as well as a safety net for when you are using other means to come to terms with your problem.
I didn't look too deeply at the link skyflyz posted, but I'm wondering if that might be mentioned there. Not as a cure, but, like I said, as a safety net in emergency situations.