I was in the high school parking lot in Florida and I just starting backing out. I was in between two cars (I swear I was looking around but I had a huge blind spot) and this blue SUV (in my opinion, way fast) comes up behind me and hits me. We both were moving. Is it just my fault, or because we were both moving, is it both?

Probably both but more the other vehicles fault and possibly the school if the blind spot is created by the parking lot design; hope you have a police or incident report from which fault can be apportioned; your insurance company may be able to handle this but you may also need to get an attorney if your insurance company is not handling the case properly