Other than honorable discharge?

So I joined the National Guard a few years ago, I was in for four months and then a couple months before I got to ship to basic, I was discharged. Why? Because Im gay, and God knows how because I never said anything, but somehow word got out and it eventually made its way up the chain and ended with me left on the street.

Other than that my record is 100% clean, not even a traffic ticket for christs sake. Since then Ive started college and completed my GE, and Im trying to decide between an Associates in Respiratory or Nursing. I would prefer to become a nurse, but, with my discharge status, is this even possible? Or should I give up hoping?
Typically an OTH discharge won't prevent you from getting a nursing license. Very few nurses are going to give a S*&t if you are gay. Good luck.