My ds was exactly like this. He was one of twins, his sister was a 'dream baby', which made me really realise that babies are born with their own temperaments. Like a previous poster he really began to improve at 8 months, almost exactly when he stared to crawl, and gradually got better and better. He is 6 now and is a lovely lovely boy. When we talk about it now we talk about how he just didn't like being a baby!!
Thing is, I really struggled when he was so unsettled, and at times I just couldn't stand the constant screaming. I regret how I reacted then, but at the time I was just so tired and stressed out.
Keep on going, things WILL improve. Try and enlist 'cuddlers' - my ds was settled for a couple of hours one time when I visited my work and the secretary who was desperate for a grandchild just whisked him off :-). I wish I had asked more people for help, I just thought I had to do it myself, and I didn't and shouldn't have tried!!
It is so hard, but trying to work out triggers if you can find any. Even now we try and make sure ds doesn't get worked up if we can, as once he is in a tizzy that's it for a while, he finds it hard to calm down!! I know it is very out of fashion, but I used a baby whisperer type of routine (I couldn't cope with twins without a routine!) and it did help - I really learned to predict when he would need sleep and feeding.
Sending lots of encouragement to you. Things will get better xxx