Tactile sensitivity is one of my primary issues but it is an overgeneralization to say that all Aspies have touch issues in the same way as it is to say that all Aspies are hypersensitive to lights or sound. Having said that, there is a HUGE difference between touching and being touched. In other words, if you are training as an EMT, you are the one doing the touching and you are in control of when and where you are making contact with another person. Quite a different thing than having someone unexpectedly tap you on the shoulder and jumping a half a mile.
So in your situation, while I'm not saying you do have touch issues, don't assume you don't simply because you are training for a profession where a lot of contact is required. If you are having trouble with relationships, it could be for a variety of reasons that are or aren't related to Aspergers. Tactile sensitivity, poor social skills or you simply haven't found the right person. In a nutshell, you sound a lot like me a few years back. I work in emergency services as well but had no luck with relationships through my 20s. When interacting in social situations, you don't have control over anything in the way you do at work where your job is to take control of every situaton you face. Interpersonal relationships have always been a sticking point for me and it wasn't until I pretty much gave up on meeting a mate that I finally found one. Go figure.