I know what it's like to completely let down your family over what they always thought you would do. I come from a big time naval family and I was pretty much destined from birth to join the naval boarding college at age 16 but missed the necessary grades to get there at GCSE.
Afterwards I did nothing for months got a boring job (at Tesco funnily enough) and didn't make any arrangements for further education, I had always wanted to be a military person and now this was all gone. I felt guilty almost like had betrayed my entire family because they had always supported me in trying to get into the navy and I had let them down.
Over the next few months in between feeling sorry for myself I read a lot and found that I had other interests that weren't what I had been so focused on for the last few years, and I can now say that pursuing those interests was way better than continuing in my self-pity (I'm finishing university next week). I can't understand your illness or specific circumstances but like me maybe if you give yourself time this summer away from your studies you will find other areas that will be exciting and interesting to you.
In the meantime it may be worth contacting the university to tell them of your circumstances, from my experience universities are getting much better on this. I really relate to you feeling like you've let down your family, I felt the same but after giving myself some time away from constant education I've found new interests and a new career which I'm excited about and feel is really my choice.