Ouch, I'm sorry to hear about this.
It does sound like what probably happened is that you got scratched and/or abraded from the fingernails and, if this partner was also rough on top of that (and worse still, without using enough lube), from that, too. That brownish discharge is likely just "old" blood mixed with discharge. Since there's not likely anything a healthcare provider can do in these instances, and it doesn't sound like you're in pain, I'd just wait it out and give your vagina some rest and TLC in the meantime. Don't engage in any kind of vaginal sex until you feel all the way better.
Preventatively is where you can do a bit more. For once, it is 100% okay to ask a sex partner to cut and file their damn nails (I mean seriously, right?) before putting them into your pants and certainly into your vagina OR to wear a latex glove to help cover their nails if they are attached to their nails. Just so you know, in case you didn't. It most certainly is also okay to ask a partner to chill out and to use more lube whenever you want, and if you want to avoid injury, things like using lube, not being SO aggressive (we live, we learn), and either cutting nails or covering them are key.
In the event things change and you are in pain, or if the rawness/soreness or bleeding doesn't stop in another few days, then I'd go ahead and give your sexual healthcare provider a call. Mind, that's also something you can do -- just call, without need for a whole appointment -- anytime. You could get their advice on this, too, by just calling in.