Yes, they most likely had a bloody fight. There comes a point when the older rooster, will be challenged and/or ousted by the younger rooster.
Attend to any bad injuries, clean them up, do not leave any blood on the feathers. Then, keep them separate. Rooster hormones are high during the Fall, Spring and mid-Summer.
Roosters are known to fight to the death, managing rooster behaviors and instincts are part of chicken keeping if want to keep one. Vicious fighting usually happens over the hens and/or lack of space. You'll need more hens so each rooster can have its own flock. Another solution is having a rooster pen, with only roosters. That will give you time to re-home.
I currently have four cockerels that hatched in September. And I have one fantastic 4 year old RIR, rooster. The cockerels will remain in the rooster pen, until they are re-homed. Until that happens, I will work with them daily, training and socializing them. Re-homing is easier if you can demonstrate that the cockerel can be picked up, even better if they come when called by name. The longer my cockerels stay, the more training they will receive.
But, that's just how I manage my cockerels/rooster. I just happen to really enjoy the challenge of raising roosters.
These are my thoughts on your rooster issue. I hope I have been helpful.
Other members will have advice, please consider them, too.