I had my first fall in November and broeke a rib. My friend's horse who I was riding spooked and when he took off, I hit the ground. There was NO WAY I could have gotten back on due my injury (not being able to breathe) and no horse to get back up on.
My biggest problem after recovering physically is being scared while riding. I did not have that fear before the fall. I have since then been thrown again as my horse just decided to act up and was not spooking (just bumps and bruises) and had to emergency dismount the last time I was on my horse. My horse and I have started training, but I am much more timid than I was before. I saw a horse acting up during a lesson the other day and got anxious just watching that horse as he was behaving exactly what my horse was doing when he tossed me.
So, I guess that said, I am officially a RIDER. As I had read prior to falling, it is not IF you fall off, it is WHEN you fall off.
As far as your injuries are concerned, I am a nurse and think you should definitely have your injuries checked out, particularly if you have trouble bending/straightening your arm.
I also hope you (and all of us) wear helmets!!!