Hey girl, I felt the same exact way as you. But I kept on doing little things to get involved like eating lunch and dinner at the house consistently. I know know know that the stress of other things (such as your grandmother) can get in the way of how much energy you have to spend on outside activity, and a sorority is both an intimidating and time intensive venture.
But here's what I did:
I talked to my Big. Granted, we have our differences and still are not on the same page in terms of many many things and we don't get along completely swimmingly. However, when I went to talk to her about me being scared and confused in terms of the whole "staying in Zeta" thing, she was understanding and talked to me for an extended period of time, surprisingly. People do care, but it is your decision to reach out. I encourage you to do so, greatly. You'll be pleasantly surprised by who you who see catch you when you take that leap.
Also, by me going to the lunches and dinners I was able to better socialize with some of the other members of my sorority. Now I have a solid group of 3 friends who make me realize why I'm in Zeta. They keep me on track academically and encourage me to do things I'd never consider before in order to better grow as an individual.
As a side note, I believe that saying "it's your fault, get involved" not only is callous but incorrect. Being a part of a sorority is not only a major time commitment, but a conscious decision to be made. How much social time do you have within an academic schedule? How well do you get along with your peers in said sorority? It's part of growing up to not only question your own involvement and if it's worth your time (it isn't, always, and GLOs aren't the answer for everybody), but, most importantly, what you're going to get out of your experience with that participation in your GLO.
Therefore, I ask, instead of callously dismissing concerns with "get involved" or "what does your family problem have to do with your GLO?" that instead we support our sister in her journey to find what's best for her because her family problems have everything to do with her involvement in her GLO in addition to other factors.
Going Greek is a different way of life - it is a choice, and a damned good one (in my opinion). One that can really really benefit you in the future and right now. However, you must make the decision to invest into it for the positive turn out and solidarity that really is the essence of a GLO (the brotherhood/sisterhood), and what we can accomplish together (volunteer work, philanthropic opportunities, personal growth for each of us). Don't decide to stick with it for your sisters, for your family problems, or because of anybody else but YOU.
Please please drop a line if you need to talk and I'll be happy to listen to you. I was in this position not too long ago and I really do empathize!
Good luck! ZL
*By the way: There was no "spark" for me with Zeta. I just woke up one day and realized how integral Zeta was to me and how much I really really enjoyed the sisterhood I had with my friends in it. I really don't know what I'd do without those gals, now, they're really exceptional! The experience is different for everybody, but it wasn't an automatic, instant love like others are fortunate enough to experience (it seems that going down this slower road is more agonizing, haha!).
Just because you and I have been initiated and know all of the rituals/secrets, etc. doesn't make us Zetas. It's something to work toward, I believe. It's about following our creed each and every day, holding ourselves to higher standards, and growing as people in this exciting time called "college"

. That's why I could never be automatically in love with my GLO, because it had to slowly mold me and make me a better person for me to realize how much I loved it. It's still a process too, by the way.