Since you got him as a chick this spring, he is a cockerel, not a rooster. There is often a lot of difference in how an immature cockerel behaves compared to a mature rooster. The problem sometimes is getting to that mature state. It is often harder on you to watch than it is the chickens, but it can get pretty physical.
Why do you want a rooster? How does he fit in with why you want chickens? The only reason you need a rooster is if you want fertile eggs. Everything else is just personal preference. Preference can be a strong motivator but it boils down to being a choice. I generally recommend you keep as few males as you can and still meet your goals. It's your goals that are important, not mine when it comes to your flock. I don't know if the right number for you is one or zero.
You had a flock of mature hens that were used to doing things their way. Now they have a cockerel whose hormones are running wild, telling him he needs to be the flock master. Is that hen in the nest the dominant hen? Often the dominant hen is the one that has the most trouble giving up power. I've had that happen before. Until the cockerel reached a certain level of maturity the dominant hen kept him in line. Then he matured enough to take over. For two days there as a lot of fighting between them, well him mostly chasing and her mostly running away, but he got in some pretty strong licks. It was hard to watch for two days but they worked it out. I have a 8' x 12' coop, a 12' x 32' main run, and about 45' x 60' inside electric netting, plenty of room. And there was one cockerel and 8 hens. Plenty of room. The less room you have the rougher it can be. Mine used a lot of my room to keep the level of violence down.
If you decide you don't want to keep him, get rid of him now. Your flock should go back to being peaceful. If you decide to keep him you can either leave them as they are now and they should eventually work it out when he transitions from being a cockerel to being a rooster. Or you can isolate him for a while and try to put him with the flock later. I'd probably give him a month in isolation before I tried again.
A lot of people make rash decisions when a cockerel is going through puberty, not realizing he and the girls will probably mellow out when he grows up, but it can be hard for you to watch them go through that phase. Since it can be violent it is possible one can really be injured. If you don't really want him, why go through that?