You are fine. I am a 5'5 Asian woman and I made a promise that I would never EVER date anyone my height or even an inch shorter. Guess what? after undergrad, I fell head over heel with a 5'5 Asian man in my anatomy class--this is just an estimation but he could have been an inch or two shorter than me; I mean who ask for another man's height especially if he is considerably short compared to the general population? We did not date since he was in a long term and serious relationship with another girl whom he met during undergrad but if he was not, we would have dated and even be in a serious relationship right now. The anatomy class was a semester long and we had a chance to get to know each other through lab times, group projects, and Facebok (the media does have a huge advantage for the dating scene). What attracted me to him was his personality and demeanor; he had an average look, he had small eyes, acne, and was a little bit muscular but I love how he did not care much about how he looked; he was definitely not Brad Pitt or Tom Cruise but I was totally okay with it. He was intelligent, academically smart, outgoing, friendly, and women dig these type of personalities.
My point is just focus on being and building yourself as a person and everything will follow
Women love men who are thoughtful and can take care of them so work on becoming that type of person and you WILL have a woman one day. Good luck!