You both need to dial it back down again.
Is she a lot younger than you? Sounds like it.
She had an accident and is feeling crap. You said it looks awful after reading up about it.
You took excellent care of her when it happened, but she was in shock and so that hasn't really registered with her.
Then the phone call. I don't blame you for being upset at her reaction, saying things about lawyers. It was unfair, but to play devil's advocate, she's probably crying and looking at her messed up face ( which will look worse in a few days when the bruising comes out) sorting out her dental bill etc and feeling very miserable.
Cut her some slack and let her get over the shock and the post-accident depression, and then both try to get over the argument. She clearly wasn't herself and when she upset you - neither were you because the accident was probably a shock for you too.
I don't think your Mum has been particularly helpful but it sounds like she was dealing with someone who was throwing a tantrum.
Do you owe her an apology? No. It was an accident. But it would be nice to say you are sorry she was hurt. If you want to maintain the higher ground, get in touch to say it was a terrible accident, must have hurt, how's she feeling etc. If your mum says it would go down well, visit with some chocs/flowers. She probably just wants to be made a fuss of. She doesn't remember your compassion at the time and is probably looking for some sympathy, why not give it to her? At least you can say "Well, I tried." This is probably more pandering than would be necessary in normal times, but she has had a nasty fall.
If that doesn't work and she's still talking lawyers, let her. You didn't do anything wrong and it would be difficult for her to sue. It's probably just bluster. It sounds like you two have a difficult relationship and it might be good to take a bit of a step back for a while and let things cool down. But at least you can say "Well, I tried."