First off cinsere, congrats on giving Bullwinkle a better home, that is very thoughtful of you.
The above information and advice is great. A few things I would like to add:
Do not punish Rocky, he needs special attention from you to show him he is just as important as before. If he gets really upset, spend time with him alone. I have 3 cats, all of which are still struggling to get along. My female Tasha, our first cat gets on much better if she is being pet and loved when all 3 are together, she gets very upset if the others are pet and she isn’t, then the growling and swatting starts. My other female Angel needs "alone" time to be happy, (I think she has middle child syndrome!
). You and your girlfriend should have both cats eating, playing and getting attention together. If they cannot do this without attacking, separate them with some kind of gate so they can see each other but still eat and play together. It works best with you on one side and you girlfriend on the other side. In short, it's a positive association with each other.
Secondly, letting cats "work it out" and show dominance is not a good idea. One or both could get severely hurt and the odds are it will not get better, it will get worse. I never leave my cats alone unsupervised as they would tear each other apart. It could take months but hang in there, they will eventually learn to coexist if not like each other.
Get you boys neutered ASAP before they start spraying. If you don't, spraying may not stop even after neutering. It's been known to happen.
Good Luck, it should work out fine, just have some patience as you got off to a bad start and that can take awhile to rectify.