I had the same problem mostly during my freshman year of college.
I thought that I looked ridiculous when I danced, and I probably did (hell most white people are bad at dancing).
However, eventually I got fed up and started practicing in front of the mirror- sounds lame, but it helped me build my confidence a lot.
After a while you realize that dancing is just syncing your movements to the beat. Every time you hear the bass thump you should be doing some sort of jolt movement and then go back to your original position in a flowing motion. Just master one step, or sway, or whatever and your golden.
No one really cares what you look like while you dance as long as you look confident doing it. If you are self conscious and feeling awkward you will be putting out those "awkward" vibes and it won't look natural.
Also, dubious amounts of alcohol helps a hell of a lot. But after you are comfortable with yourself, you won't need the alcohol anymore.
Hope this helps.