Have you discussed with your mum what it is that she is worried about? she may be worried that you won't cope on your own, she may feel protective or she may just think that she won't be able to cope without you around. try explaining to her, depending on what it is that she is worried about, that you really want to go, this is an amazing opportunity for you, it'll give you a degree, etc etc. Yes, univerisity is all about meeting new people and doing things you have never before had the opportunity to do, but you can still call home as much as you need to and even visit (if your uni's not too far away). You don't lose contact with people from home unless you choose not to contact them.
At the end of the day, you need to know what it is that your mum worries about, and try to reassure her or even compromise on issues. If she knows you are going to be happy and healthy, then this will lessen the stress and will put her mind at rest. If her health problems are stress related, this will help, too, but I'm not a doctor!
That's just some advice. I hope that's not patronizing! What ever you chose to do, good luck!