I have a very sensitive child as well, he has been "difficult" since he was a baby and he is really going through a stage right now that is very very trying, he is 27 months old. So here are my thoughts, of course I don't think the same things work for every family but this is what has at least helped with us.
Maybe eliminating the nursing all the time so that he is not able to demand from you all the time and starts eating other things, night time nursing is a comfort thing but maybe no more mornings and nap, like I said just a thought, you need to feel less drained and maybe he would get in to the habit of it being a night deal and like I said start eating a bit more.
I have used the stairs as our corner a lot lately, my son will start the screaming/crying where he won't stop and I have elminated everything else besides the fact that he is being fussy... usually I say something like "I can see you are having a difficult time organizing yourself how about you sit here until you can do that?" and then I put him on the stair, sometimes he stops immediatly and sometimes he screams harder for a while. I am never out of his line of sight so he does not have to be afraid that I have left him and if he gets up before he has calmed down I just silently return him to his step. It seems to work for us and he has learned to start "organizing" himself which is what it seems with my little guy, he likes to organize everything, even his toys so he sometimes (ok, so right now a LOT of times) needs time to get himself together.
Just some thoughts and (((HUGS))) because I know it is a really hard.
As a p.s. I personally think that unless you have some hard evidence that there is a food allergy then it is just going to put more stress on you trying to avoid certain foods and taking away the only foods that he does eat. Just my thought though.