I had the same "symptom" with my first....
For the first 6 monhts of his life, my son would LITERALLY sleep no longer than 20 minutes at a time, three hours consecutive for the day. He screamed nonstop. There were several reasons with him, which I'll outline, but it only stopped when I put him on Alimentum from Simmilac, a completely synthetic formula.
Initially, the screaming was a result of hunger - I just couldn't seem to make enough milk. Once I gave him his first bottle of formula, at about four weeks, the insistence of his screaming lessened a bit. The hunger was satiated.
He also was born with a hernia and reflux, both of which he still has at almost-seven. I try to limit his intake of dairy while making sure he drinks enough to get the calcium he needs - which is hard since he loves milk and sneaks it every chance he gets. My sister (at 30) has had reflux all her life, though, and has had several operations as a result thus I am scared to let him have too much.
Finally, he was born with TONS of allergies, tho by five he's grown out of most of them. He did have a milk allergy initially, but that was resolved by three.
Don't worry - it won't last forever, but having just had another one a year ago yesterday, I know it sure seems like it!! If you have to demand that your husband take him, do so - you need sleep and good mental health to take care of your babies. As a single mom, I hired a babysitter a few times and asked my parents to watch him a few times just so I could sleep. If you have family close, try that too. You need a break from the screaming. And when all else fails, put him down in his crib, close the door, and walk outside for a few minutes. It seems cruel but he's not going to stop crying and again, you need a break.
Not that it ever worked for us, but try gripe water, and read The Happiest Baby as previously suggested. And I would try formula supplementation and if you already are, try alimentum. It's expensive but given the change in my son after we switch to it, well worth it.
Good luck! And don't listen to the old biddy who told you you were spoiling your newborn!!