pugsmum, my second ds was like yours.
he used to scream ALL the time. in fact, it wasn't even a case of he would only sleep on me, it was a case of him just screaming for hours and not feeding or sleeping!
i honestly do know how hideous sleep deprivation is. trust me. he fed every 45-90 minutes day and night until he was over 9 months old!!! 
This sounds like hippy crap I expect, but it truly worked for me.
Once I accepted that this was how he was, it got easier. I read a book called the happiest baby on the block, by dr harvey karp, who explains why babies cry a lot, and why they want their mum all the time.
and somehow, knowing WHY he was behaving the way he did made it easier to bear. knowing that there was light at the end of the tunnel (tho it didn't always seem it) helped too
and like a previous poster said, sometimes it helped just to get someone else in to help me. sometimes that was DP just taking him for half an hour, sometimes it was a friend coming in and holding him while i had a nap or did something with ds1. sometimes it was going to my mums and listening to what she thought and letting her have him while i slept on her sofa!!!
looking back on it now i can say it's one of the hardest things I have gone through in nearly 6 years and 3 children.
But I can also recognise that actually it's such an unbelievably short length of time in the grand scheme of things.
all the other stuff that needs doing... it can wait, esp if he is your first and you don't have other kids to take care of.
he needs you right now, and he is so, so, so very young still...