H.,
I went through this same thing - and am still going through it. My first was a perfect textbook infant. She slept for six to seven hour stretches at two months, had very little throw ups, was easily sated by using the "Happiest Baby On the Block" methods. Good sleeper, good eater, happy all the time. She was a dream.
Two and a half years later, came Sam.
He's been a high maintennance baby from day one. He is a light sleeper - rarely more than an hour's nap. He wakes frequently - only lately have we been able to get more than five hour stretches out of him. He's restless and demanding and I've been thrown up on more times than I can count with him.
But when he reaches out and smiles at me, I know it's all worth it. All babies are different, as are all people. You can't really count on the second baby to be anything like the first. And more often than not, siblings end up being polar opposites of each other. Having to care for a newborn while you are still meeting the needs of your first child takes more patience and strength than anything I can think of. So cut yourself some slack. It's hard work!
If you've exhausted everything - swaddling, shusshing, rocking, white noise, vibrating bouncy chairs ... I guess the only thing I can suggest is a change of venue. Weather is getting warmer, try a bouncey chair outside. Or the car. Or a playyard in the backyard.
As far as letting him sleep on his stomach ... I am not going to be the one to say it's okay. But just so you know, my 9 month old slept with a blanket - also taboo - since he was three months old. It's his lovey and as much as I know it's not a good idea, I know he sleeps better with it. And there are many women on this site that say they've allowed their infants to sleep on their stomachs because that was the only way the little guys would sleep. So, no, don't allow it (nudge nudge wink wink).
Good luck to you and your family. It gets easier, I promise.
J.