I agree with tkmaxx. My ds2 is 13 weeks and has just, in the last 10 days or so, started to settle on his own and sleep away from me for more than 20 mins at a time. I know it gets better because i've been through it twice before but it's still a tough time.
a couple of things that might give you a bit of a break:
have you tried swaddling him tightly, then snuggling him up in a bouncy chair with a t'shirt or something that smells of you? That's fooled all of mine for a little while.
Sleeping propped up on lots of cushions with him on your chest, while not ideal, can help you get a little bit of a sleep.
I used to go to bed once he'd had his early evening 7/8pm ish feed and dh would sit with him until he wanted another feed so I got a couple of hours sleep in.
Have you tried a pouch sling? One of these type . They keep the baby in a more natural, curled up position than the Baby Bjorn type ones but leave your hands free to get on with things while the baby sleeps. They take a bit of getting used to but ds2 loves mine.
Honestly don't worry about him getting into bad habits yet. My ds2 used to always fall asleep on the breast and refused to take a dummy but he now feeds, has a dummy and goes to sleep. It's amazing how much they change when they get to 12/13 weeks.
Someone on here, I forget who, talks about a 4th trimester, which is the theory that babies should still be inside us for another 3 months but, because we walk upright, our pelvises couldn't take the strain so they are born earlier than they need to be. So the first 3 months of their lives they behave as if they are still inside us, needing to be close to our bodies, hearing our heartbeat. He's really still so tiny, he doesn't even realise the umbilical cord's been cut and he needs you close to him, it's hs survival instinct, keeping him sfae from predators.
Make the most of this time, I know it's tough and a bit frustrating when you've got a demanding little being permanently
attached to you but he won't be tiny for long and I guarantee that there will come a point when you'll wish you had these early days back again!
Sorry, thisis a bit waffly, I'm expressing and struggling to multi task with my sleep starved brain!!
Hope some of it helps anyway.