This post is the most heartbreaking I have read on here for a while, I am so sorry you are going through all of this OP, you absolutely have the weight of the world on your shoulders.
I would not be at all surprised if your physical symptoms are caused by stress, you are under so much pressure and have so much going on emotionally.
It sounds as though your issues are two-fold; 1- you need some help processing your grief for your mum 2 - being your Nan's carer is ruining your life and something has got to change. You have literally sacrificed everything by the sound of things - your chance to meet a partner and settle down and possibly have children, your chance to have a fulfilling career, your chance to have a decent social life, and actually on a more basic level you have no choices day to day about how you spend your time - I cannot imagine how hard all of that is. You are 32 and should be planning and living and you are trapped. That would make anybody ill, you must feel utterly miserable. And because it makes you feel so isolated and alone you naturally are yearning for the comfort of your mum.
If you stopped doing the caring role, went on strike as it were, and contacted the local authority they would surely be duty bound to step in? And your Nan will have to understand, that although she may not want outside help, your life is literally being ruined and she cannot continue to take every bit of your time and energy any longer. I mean let's be hypothetical - you are a young woman, what would happen if you got pregnant and had a baby, then what? No way would the situation be able to continue, baby would have to come first, your Nan's care would have to move to somebody else - what would that be in that situation?
I think you should see a different doctor, can you be 'signed off with stress' as it were from your role as a carer and then take that to the local authority and demand that they step in with some help? If the doctor were to say you are too fragile physically and mentally to continue then that's that.
I really feel for you, you should not be in this position. Yes your Nan needs to be cared for, but you need the freedom to live your life too, it would be awful to look back and have regrets.