Classic case of OCD as far as I can tell.
I had a similar problem, but not with people (most people anyway). I wouldn't touch certain objects that just seemed plain dirty to me. I tried this technique I read about where I touched a public toilet and didn't wash my hands. It was gross for MAYBE 15 minutes. Afterwards I was talking with my friends, and while I initially avoided touching my face, or them, or most anything for fear of spreading my "contamination", I quickly forgot it all. About a half hour or so later I was even eating lunch without washing my hands.
I did this excercise a couple of more times, and eventually realized one day that I had went to the bathroom, PUT THE LID DOWN BY HAND (something I REALLY had to force myself to do) and flushed it BY HAND without even realizing it! Sure, I washed my hands, but not excessively and it wasn't until I was leaving that I realized I had just done that without thought. I currently do this all without having to be like, "Whoa, did I just do that?!". It just happens.
Perhaps that could work for you. Just DO IT. Shake people's hands. If you feel you're going to absolutely FREAK OUT or something, go and wash your hands and calm down a bit. It really wasn't that bad for me though, I guess just as long as you stay active right after--socializing (probably best), watching a movie, excercising, reading. Something to make your mind forget that you don't like that, and then your mind won't associate touching other people with germs.
At the very least, constantly use this techniques on those who you would like to pursue a relationship with
Wouldn't want OCD getting in the way of that.
If this doesn't work at all, perhaps try seeking out a therapist that specializes in OCD therapy to give you better techniques.