Judgin by the sound, and the wheel wobble, my guess would be you have a broken spoke - those are the metal sticks that extend from the rim to the center - somewhere. That being said you also might have a problem with your hub. Now with that being a most likely 3 speed internal shifting hub, it depends on the shop and what’s wrong with it, but you [i]might[i] be able to get that fixed.
"Steel is real."
- IDK, some guy.
Without knowing all the specifics, but taking into consideration that there was excess weight borne by the rear hub, there is a chance that the hub axle is bent a little. This would best be determined by removing the wheel from the frame (chain off sprocket) and turning the axle by hand (about 5 minutes work if you have the tools; a very quick job for a bike shop). You can leave the cable attached, but I would disconnect that also, but first marking it for reconnection if you are taking it apart at an adjusting point. A bent axle will be felt binding a little bit (or a lot) upon turning, and it also may be visible if bent enough. I would ckeck this first before spending time and money truing the rim and replacing spokes since it will eventually permanently damage the hub if not rectified. I have no idea of how old the bike is and if the hub has a sealed, or cup & cone bearing design (what is the bike, the year, and hub make?). If a bent axle, it would probably be cheaper just to replace the entire wheel assy given the parts and labor costs for the hub repair, as well as the rim/spoke repair.
I doubt the shift cable needs afjusting if no hub damage unless it was not properly set-up prior (was it shifting cleanly before?), or the cable got stretched resulting from the accident; still nor a bad idea to verify. Did the bike hit the ground on the cable side of the hub possibly damaging the outer hub mechanism?
Good luck!
Ride Fast, Be Safe!
Howard