How to solve guilt and anger?

I've always relied on my family until a few years ago. I find it difficult to make new friends and open up to people, and I never developed very good social skills. That was okay for a while, but for several years, I've found that I can't really trust or rely on emotional support from my family either. There has been a lot of tension at home, and I often feel like I'm incompetent and not doing enough for my family members.
Recently, the only person that I used to really count on and who I could be myself around basically let me know that I had let him/her down big time by being unreliable and got super mad. I feel awful! She/he has serious mental & some physical health issues that I find hard to respond to, because he/she is so tough-talking/we don't have a sentimental relationship.
I feel sad and guilty for failing someone I care about, but at the same time, I feel angry, even though I think I shouldn't. I have no one that I can fully depend on, so I feel resentful when others expect me to be fully dependable.