Do NOT give up your course, you will regret it forever.
Treat "sorting out mum" like you would a degree project!
Write everything out as if mum isn't a relative, really dispassionately.
What is wrong with her?
What exactly does she want?
Have Social Services done a Needs Assessment for mum?
Have you had a Social Services Carers Assessment?
How old is she?
Does she own or rent her home?
Do you have siblings?
What does she need?
How is it going to be paid for?
Do you know anything about her finances?
Do you have Power of Attorney?
Is she claiming Personal Independence Payment (assuming she is under 60).
As for the comments of others, just ignore them.
They will be upsetting, but you have to understand their underlying motivation.
If you do something, they won't have to. They will all be wearing what we call "Teflon Raincoats" trying to let everything slip off their shoulders, so they can avoid their own precious lives being affected!!
Come back here whenever you want, you'll get lots of support from me and many others.
I was widowed when I was 54, and then disabled in a car crash (not my fault) 3 months later, unable to walk properly for years.
Mum has to face her new life, work through the pain and grief herself, she can't bury her head in the sand or use you as a substitute dad. You are young, bright, intelligent, if you have got to uni, don't waste your life.
There is a lot of help available for mum. It's HER decision what she does from now on.
It's YOUR RIGHT to choose not to care. Don't give up you studies.