It sounds like you did a great job. You stayed calm and were assessing what it could be, having good instincts about what to do, and what could cause more harm.
I've had 2 recent crossings with injuries in the last month, so I'm also wishing I knew more. Both were bike crashes. One at a race, and I drove the guy to our lbs where he ended up getting a ride to the hospital from the team manager; then a couple of weeks ago, a little girl fell in front of my house. Her screaming made me run out to help her, and I grabbed my cell phone, which was all I could think to bring. Her mother was to her before I was, and started trying to get her to stand (which seemed wrong to me). Her screaming got worse, and she couldn't stand. Her father came and carried her home, but by this time I was pretty sure her leg was broken, and asked if they wanted me to call an ambulance because I thought she shouldn't be moved. Well, they carried her home, telling her "it's just a scratch". Turns out her leg is broken. Poor thing.
I ended up looking up info on what to do for a broken leg, and now know (I know this is the bare minimum, but it's still more than her parents knew) to splint (use a wooden spoon if that's all that's available) before moving. So many other things can come up that I'll be of no help with, I really should take a first aide class.
'02 Eddy Merckx Fuga, Selle An Atomica
'85 Eddy Merckx Professional, Selle An Atomica
'10 Soma Double Cross DC, Selle An Atomica
Slacker on wheels.