I agree with Will, Gareth and Ekona above - this is going to be a difficult time for you mate, but you have to think that you and your mum only have each other. You gotta sit down and talk it out and keep your best to stay calm. It's easier said than done though. I agree with Gareth that as a parent it's your duty of care to look out for your child (no matter how old they get), but at the same time as their children we also have to look out for them.
In my family we don't see money as "mine and theirs". Yes we have our own bank accounts and own income, but when it comes to paying for stuff for each other we just see it as "family money". That way nobody feels like they "owe" anyone anything. And let's face it, as a family we shouldn't have to "owe" each other anything - it should be done for the love of your parents/children/siblings (even though at times they p!ss you off to the max).
Ekona's right in saying that you need to confront your mum and lay the cards out on the table to her. She probably is feeling embarrassed about the situation and she's lashing out at you coz you're the only one there. See past her blaming you and see the emotional pain she's also in. I still don't think it's right of her to blame you for this, but it's how her mental state is at the moment.
You guys will work it out - blood runs thicker than water Matt.
But sometime distance will also help. So if you can afford it, get a place of your own to rent, or flatshare or something while your mum stays with your nan. Let her realise how much you do for her, let her miss you.
Different situations make people change, and hopefully in your case for the better.
Hope it all works out for you in the end bud - you're a good guy