There's been some good advice already, but I want to show a different approach. First, to the poster who recommended spanking, please rethink this. Even the American Academy of Pediatrics recommends against spanking, as the evidence is clear that while it may bring about the desired result in the short term, it sends very strong negative messages (eg, that it's okay for bigger people to hurt those who are weaker).
We had some issues like this when our second was born. One thing that helped me was realizing that, in contrast to the baby, she seemed so much older and more mature that I was expecting too much of her. Most toddlers regress some when a new baby comes, and it is not under their control. So, things that she could do at one time may not be possible another time. Sometimes she needs more help than I think, but doesn't know how to say that. Also, the connection between right and left brain is not fully developed, so kids at that age are not entirely able to control their impulses or connect judgement/reason with gross motor control. So, even though it is so hard when you have a new baby, bringing as much patience and understanding and helpful attitude to the situation will go a long way.
So many people stress the idea of sticking to your guns with children, but I often don't parent this way. Maybe if your son is very strong-willed and spirited, what he needs to see you model is willingness to compromise, flexibility, and creative problem solving that emphasizes solutions that can make everyone happy. Staying calm helps too, and some irritating behaviors like screaming really will go away if you just ignore them. It takes a lot more time and sometimes I am so tired that it's difficult to think straight enough to figure out how to really solve a problem, when I wish she could just do what I say. But now when I see her trying to understand why the baby is crying, or comforting her, or "reading" her a book . . . I know she is doing these things out of kindness, not because she knows that big people approve of these behaviors.
Many many people will tell you that if you don't strictly enforce rules your child will become "spoiled" and manipulative. But I can honestly tell you that our daughter is making so much progress these days, I am so proud of her, and when people compliment her behavior in public places, it's just a bonus. Recently she went to her first funeral, and it was a stressful day for everyone, but more than one person commented that she was the best-behaved child there.
Good luck! And if you have any questions, feel free to message me.