OP my son was a rubbish sleeper and I know how you feel. Personally I was not willing to do controlled crying. Sleep did improve a little when I night weaned him (actually he slept through for the first 2 weeks after night weaning, then went back to waking every 2 hrs - aaagh!) It got a lot better, to only 2 night wakings, when I did gradual retreat so that I was sitting by the door with him in bed but able to see/hear me.
In my family babies seem to grow out of night wakings at age 3 and nothing (not even controlled crying which my sister tried) helps our babies much before then. Some babies are just shit at sleep, it's in the genes.
I would suggest you try to night wean him and see how that works out for a few weeks. Eg stop feeding in the bedroom but allow on demand feeding anywhere else, if at all possible have dad cuddle him to sleep so he can't smell milk, or put a cushion or something as a barrier between your breasts and him as you cuddle. If that doesn't help try gradual retreat. It can help a lot having baby learn to sleep without physically touching you, but that doesn't mean you have to leave him completely alone, controlled crying style. There's a huge difference between him crying because he's angry at you and crying because he's alone and afraid.
If those don't work it's up to you if you do controlled crying, personally I don't agree with it but perhaps more importantly it does not work at all on very stubborn personalities, some people try it for weeks with no success, others find it helps in a couple of days. Many find it's a temporary fix but then things go back to how it was.
What saved my sanity was giving up on the cot and cosleeping on a floor mattress, with me sometimes going to bed with him, at 7/8. Shit obviously but at least I could function - and actually some of those night time cuddles were total bliss.
Good luck, I know how hard it is and the toll it is taking on you. Try to remember that your baby is not being completely unreasonable - his teeth hurt and breastmilk helps them feel better, and his survival instincts tell him to keep mum close at all times and yell to her if he gets separated. For millions of years that was the main reason humans survived.
Good luck and big hug. It will, one day, be much easier than this.