I do apologize that we are playing a bit of timezone tag.
Anyway, I would say that it is understandable that she isn't keen to have this handled, as it will be sore. And if she is tender, I'd be suspicious of at least some bruising along with swelling from the constriction (which will continue to reduce now that circulatory flow has been restored). Though we do need to keep a close eye on this over the next few days since your worry is a valid concern. Long term occlusion of the blood flow to tissues can lead to serious damage and sloughing. But since the swelling sounds to be reducing already, we' d hope that this will not be the case for River.
So, in regards ***** ***** we can do treatment-wise, we'd want to rest her in a small deeply bedded pen with easy access to food/water. As well, I would advise treating her with a non-steroidal anti-inflammatory (ie Flunixin, Banamine, Meloxicam, etc). Just to note, I would avoid Aspirin (since it is a blood thinner) in this situation. And while there is no indication at the moment, you could chooseto cover with a broad spectrum antibiotic to cover bases (just in case we have had a microscopic tissue breech) but that would mean discarding her milk. So, that is at your discretion based on what you are seeing here.
Overall, this doesn't sound severe and therefore we'd want to medically manage her discomfort while monitoring her over the next few days. Do keep an eye out for any furthe discoloration or changes to the skin. As long as we don't see those, we'd expect this to normalize, heal and become more comfortable for her to walk on again.
All the best for River,