You will have to make sure either the neighbor keeps their bird up or keep yours behind fencing, but be aware that fence fighting can take place.
It would be a good idea to approach the neighbor and kindly ask them about their flock.
Your rooster has taken some blows to the head, neck, breast, etc. It's going to take some days to recover. Head trauma can take a while, his eye says a lot along with the facial swelling.
I would continue with Triple Antibiotic for his wounds. For the eye that is closed, open it, flush it with saline and make sure it's still intact. Put a little triple antibiotic ointment in that eye. Just let a dot melt into it.
Check his breast and crop area to make sure there's no punctures. You may find bruising (green skin). If there's abrasions or broken skin, then apply a little triple antibiotic ointment.
Sugar water is good, alternate to fresh plain water too. If you have poultry vitamins direct dose him once a day for a few day.
He may have some cuts inside his beak and he's sore. Offer him some wet feed. A little scrambled egg may be enticing. See if he will eat a little something after he's well hydrated.
How do his feet look? Any damage?