I think that screaming is just a phase that your baby is going through. One of mine (I can?t even remember which one) used to do this. My approach, especially in the middle of the night, was to shut him up and go back to sleep.
I really don?t think you need to worry about giving in to a baby so young. There are so many things that we have to say no to at this age because of safety that he will never think that life is all his way.
As he goes older and can express himself more easily you will find he uses other ways instead of screaming to communicate with you.
Best wishes,
Barb