First, and most importantly, what size of tank do you keep these in? If it's any smaller than a 40 gallon, this might be the reason why they're aggressive towards eachother.
You should also test the water parameters to see if the water is okay. That's important for the fish to recover in the first place! Test the pH, ammonia, nitrite and nitrate. pH should be around 7-8, ammonia and nitrite should be 0, and the nitrate should be as low as possible! Anything above 50ppm might be harmful.
Red lips can be a sign of mouth rot, which is a bacterial infection, and should be treated with an anti-bacterial remedy, naturally
And you should absolutely not leave their wounds untreated! They might end up infected with fungus or bacteria, which may be really dangerous |:
So for now, I would suggest the following:
1. Test the water immediately!
2. Buy some medical salt and dose it according to the instructions on the package.
3. Add an anti-bacterial remedy, usually on this forum Melafix is recommended.
4. Wait and see if the fish are getting better, observe their behavior and make sure that they eat well.
And do tell me the size of your tank, and what kind of filtration you've got (: Other than that, good luck with your fish!