This is a tricky situation to be in, and i guess most carers have felt like running out at some point, i know i have felt like it many times.
Nobody can tell you if it's best to move out or not, that is a decision you have to make for yourself. But always remember that your health is very important too, and you must take care of yourself too.
Have you told the doctor or nurse that your mum has got worse? If not I would say that is the first step, and tell them that your mums illness is making you feel ill too, let them know that you are struggling to cope, tell them exctly how you feel.
Perhaps you have a social worker involved with your mum, tell them what's going on and they might be able to do something to help.