Whew! I just got a call from my apartment complex. The pest control technician went to my place and brought the captured spider back to his shop. They looked at it and said it's a yellow sac spider. They do bite, and can cause skin irritation, but nowhere to the dregree of recluses. They also scheduled me for next Friday to have my apartment treated by their exterminators.
So I guess I was right about the bites I've been getting as they said the yellow sac spider is in fact a biting spider, and it does have venom, but mostly resulting in skin irritation. I can deal with that and go on the hunt for these little devils!