You need the help of your HV, midwife or doctor because that sounds terrible.
Does he take a dummy instead of feeding constantly? I had to hold the dummy in my sons mouth for the first 4 months until he got the hang of it but now he finds it a great comfort and it gets him to sleep. He loves the action of sucking on something so would otherwise be on the boob or bottle all day/night. I was just careful not to let the dummy interfere with feeding on demand, if he seemed hungry even with the dummy in I would feed him.
If you are breastfeeding is there anything in your diet that seems to make him worse? Spicy food, garlic, dairy, caffeine? I think these are all thought to go through the milk to the baby.
If bottle feeding are you using a suitable teat, could you switch to faster or slower flow or a mixed flow? Have you tried a different type of bottle or an anti-colic one? What formula is he on, perhaps it doesn't agree with him.
Can you tilt where he sleeps so that his head his higher than his feet (slightly!) to help reduce what he brings up?
Sometimes babies do well in a sling where they can be upright, have you tried this? I walked around and around my kitchen singing to the baby with him in a sling (often with a dummy in) and he would go to sleep.
Is there anyone who can give you a break? You can't function on zero sleep.
You say all you know how to do is feed him, and that is a pretty major part of his life right now, but have you tried singing, taking him out in the pram (does he fall asleep then?) putting him in a bouncer or swingy seat? I would put mine in a vibrating swing chair and hold the dummy in and that saved my sanity in weeks 5 - 12 as he would go to sleep beautifully somewhere that wasn't on me.
Sorry if none of this is useful, just trying to think of all the things I did when mine was that age. It does pass though - my son spewed up what seemed like everything for months but gradually got less and less sick. After about 4 months he hardly needed winded and was hardly sick.