I'm not a baby person and I found the time when the children were very dependent on me very difficult. So I went back to work as soon as I could and found someone to look after the children who did enjoy babies and dependency and thought it was lovely. I have loved my children more and more as they have grown up, and now enjoy spending time with them, but I recently had a SAHP period again, and found it almost as depressing. So I'm back to work again and enjoying it, and dh is the SAHP and loving it.
It really is OK to say I'm not cut out for this, and if you are turning into a screaming banshee then you probably should.
So, why can't you go back to work? What could help that happen? Can you get the help back again to sort out the sleeping (I would so hate that - no independence even in your own bed - poor you)
Could you get extra help in for a little bit to sort out the sleeping issue, or just to give you a break. Toddlers are clingy I think, but unless he has some more people in his life that may not improve. If you are losing your temper and screaming at him then he may be feeling insecure and therefore more clingy, so I think that even if at first he finds it difficult to be separate from you in the longer term it is probably what you all need.
Work wise are there jobs you can apply for? Would your family finances be OK if you worked and your dh didn't? Or if you both worked part time, could you afford a childminder or nanny (or nanny share)? Could you do something part time and your son go to a creche or nursery (if you put his clinginess on one side - the right carer could overcome that).
To me the important thing is that you don't think that somehow you deserve this, and that things can't change. They can, and I think they need to. But please don't think that you are a bad person or even a bad mother for not enjoying babyhood. Maybe you will be fantastic with teenagers!