I really feel for you as I went through this aswell and it was a hellish time for us all tbh - it does pass but it really does feel awful when you are in the middle of it 
Ds1 was 2.4 when DS2 was born and he suddenly changed from being a very happy, smily child to having tantrums, biting DS2, hitting him etc (but on the flip side, he was totally obsessed with him and wanted to be near him all the time and wanted to know where he was etc). DS2 spent a lot of time in a travel cot in the lounge when DS1 was around as it was the only place DS1 couldn't reach his fingers to bite ...he still threw things in though!
It also seemed to coincide with DS1's sleeping habits going to pot as we had moved him into a bed just before DS2 was born and he refused to stay in it and would be up and down all night (although, in hindsight, i do wonder if this was due to the fact that me, DH and DS2 were all in the same room whilst he was by himself in another room?)
Anyway, I posted on here several times in despair and got lots of responses of 'it passes', 'they will totally love each other' etc etc.....and it is so true. DS2 is 2.7 now and they do completely worship each other and what happened just seems like a bad memory.
I think the usual 'ignore the bad behaviour and praise the good behaviour', would work and just make sure that DS2 is kept out of harm's way as much as you possibly can. I had it slightly easier as I kept DS1 in nursery 4 days a week so me and DS2 could have a lot of 'bonding' time so I didn't feel bad about putting him in the travel cot when DS1 was around. I also tried to make a real effort to spend some 1-2-1 time with DS1 by DH taking DS2 out or me taking DS1 out.
Oops bit of an essay but I clearly remember how bad I felt - I think I was just so upset that DS1 did not totally adore DS2 as much as I did (why would he though??) and used to get really annoyed with him for hurting such a small, helpless baby 