as dandylin said, my automatic response to everyone is "I'm good" or "I'm ok" even when I have tears in my eyes and I should be admitting I'm not.
I'm sorry your sister makes you feel like an inconvenience. that's a really crappy position to be put into: care for your sister's convenience or your own health. If you feel like you would be a danger to yourself without going in, maybe you should reconsider your t's idea of going inpatient. It kinda sounds from your posts like you are leaning towards going inpatient if it wasn't for being an "inconvenience"... maybe you might benefit from a short stay?
I went a few times when I got no visits because my wife had to take care of herself, and it was a really long drive to visit me. I remember feeling really lost and alone, but at the same time it was nice not having to put on a face for her visits. I could just work on pulling myself together.
I'm sorry your family doesn't show they care. ((hugs))
Can you take your T's care and internalize that? I know it's not the same, but it's still caring for you. Maybe it can help ease some of the hurt just a tiny bit?