Your baby is probably going through a growth spurt, and I know it can be insane, but he's just starving all the time because he's growing so fast. Your older son didn't do this because formula takes longer to digest so he wasn't hungry as often.
You don't have to wean the baby unless you want to. If you have someone to look after your older son during the day, just crawl into bed and take the baby with you. Spend a day or two there and get caught up on your sleep. The baby can nurse on demand while you're resting. It may even build up your milk supply enough for you to pump and store some milk for later, when you need to be away from the baby, or for his dad to give it to him during the night so you can sleep.
If you can't do the bed thing, then it won't be the end of the world if you have to supplement your baby with formula once in a while. If the baby's dad can give him a bottle during the night, it will benefit everyone. You can get caught up on your sleep, your baby may sleep a little longer and can bond with his dad, your 8 year old will have a more energetic mom, and your baby's dad will get to know his new son.
Best wishes to you, I hope it works out.