Please don't feel guilty about this. You are not lame! We all have bad days and if you live with anxiety then you probably have more of those days than most people. I get that feeling quite often. I just want to go home, curl up on the sofa and be in my safe place. It's a pretty normal reaction when you are feeling anxious, so please don't beat yourself up about it.
You obviously are a wonderful big sister to be so concerned about your little sis and I'm sure she had a fun time. Does she know about your anxiety? I find that telling people close to me about my anxiety disorder means they are more understanding when I have an off day. When I say to my partner "we are going now" he knows to pick up and leave and get me home (the sweet soul hardly ever complains either!)..
Please don't beat yourself up about this okay? Have you tried any counselling or CBT (cognitive behavioural therapy) around these anxiety issues? Both have helped me out enormously, especially when I am at work for 10 hour shift and I just can't go home. Take care, let us know how you are going.