Let me give some advice from a fuzzy one. My beard first started to come in when I was 13 years old, but it was definitely not symmetrical. In fact, it was a few years before any fur started to grow on my chin... I had a REVERSE goatee. I still have a small patch on my chin where no hair grow.
Basically, when you are getting hormones, through shots or through puberty, it's gonna cause havoc on your body. Things won't be symmetrical to start with. Sometimes things will even be different color (when I was a teen parts of my beard would come in grey, some would come in blonde, some would come in dark dark brown). In the end it evens out. If you want to grow a full beard, it takes a while, because not all parts of it grow at the same rate.
It is pretty much impossible to grow a beard without at some point looking like you have the mange. That's one of the great things about being a guy I guess...