Physical stature and confidence do go hand in hand, like any fact there are exception to the rule. But as for short and shy, that would be a yes, lol.
You'd do well to stop trying to blame this factor or that factor for your perceived failures or shortcomings in the social/sexual arena. There are plenty of short guys out there who get laid like crazy. There are plenty of nice guys who get the same, as well. I believe you that you have a lack of confidence, and I'm sure that's a significant factor behind why you are still a virgin, but the only way you can fix that (and it is fixable) is to focus on positives and areas that you can change. You can't do anything about your height. Accept that this is not as big a factor as you are making it out to be and move past that and you'll be on the right track.
As DC already pointed out, I'm 6'6", and the generalizations you are making about tall guys simply are not true. I lost my virginity while still in high school but I'm absolutely sure this had nothing at all to do with my level of self-confidence (I had none). I also didn't start having a lot of sex until the last few years. I attribute that mostly to practice dealing with the opposite sex and determination, as I haven't really changed that much as a person in the last ten years.
I sympathize with your feelings that nice guys always finish last, as a nice guy myself, and in certain situations, in cetain social circles, and with certain types of girls... it definitely seems true that the guys who act as you would think an "asshole" would act have much better luck with the ladies... those guys that are extremely outgoing and assertive. However, you can make your "nice" qualities work for you. It just takes practice figuring out how to steer a relationship in the direction that you want to take it, figuring out how to send out the correct signals and avoid sending out the wrong ones, et cetera. There are plenty of people out there who like nice guys.
I think what njqt said about you simply being afraid of sex is a load of crap and offensive. Speaking as someone who once had a very difficult time finding sex I always HATED it when I heard from someone else who didn't have this problem and seemingly couldn't possibly understand where I was coming from say that I just wasn't trying, as they assumed that everyone should have as easy a time as they did getting laid. It doesn't come that easy to some people. On the other hand, I think you are shooting yourself in the foot judging by a lot of the things you are saying here. It sounds like you have a very defeatist attitude.
I'm using heterosexual terminology because that's where my experience lies. But I think most of what I said above can apply to same-sex relationships as well.