I've just caught up with this.
As amazing as you have been, it is time to think about you and put yourself first. My worry is that you are only young once and once it's gone you will never get that time back.
Care homes not only provide excellent physical care but also mental and healthy social care. What I mean is that it could mean a new lease of life for your gran. They provide regular entertainments, and opportunities for trips out (if the resident is able to of course). These homes do exist as my mum is in one, although unfortunately she is too far gone to get the most out of their daily activities.
You say the homes in your local area are appalling, so look further away. It doesn't matter where it is (within reason) as long as it's the right one.
It sounds all too easy doesn't it? Well it isn't, it's one of the hardest things ever, but you are waiting to exhale and I honestly believe if you continue to carry on the way you are you will be no good to her at all because you will be to ill to care for her at all.