The way I see it:
1. Making friends isn't even remotely close to a line. The line is way out in workplace romance and sexual power politics land. The very basic mitigation strategy you have is simply not to go there. If you can't not go there, then you have other problems to deal with first, and the sooner you go about that the better!
2. If making friends isn't crossing a line, it's therefore not sticking your neck out at all.
3. There is no more liability than any other workplace friendship, and just as much potential for gain as any other workplace friendship. Plus, if you are socially awkward as you claim, you know darn well that the potential for gain is ginormous. If it's hard for you to make friends, you need all the good friends you can get!
4. I'm sorry you had a bad experience with nursing, but it's silly to hide behind that as an excuse. You need to get on with your life.
5. The less you put women on some weird fetishized platform of unobtanium, and the more you just treat them as fellow humans and geeks, the less likely you are to cross a line. At least, that's my conviction, and it seems to work pretty well.