I was double booked once before and I felt like you're feeling. I was on time but I sat and waited and no T. I waited for about 40 minutes.
A couple of times my T said she'd call me to make our next appointment for various reasons and when I didn't hear back from her I felt really awful too.
It's all so important to me... but a week can easily go by without her thinking about me or remembering that she hasn't seen or called me that week.
When I mentioned this to her she told me "I didn't forget about YOU just the arrangement."
Talk to her some more about it.
She did forget your appointment time but I bet you're not nearly as forgettable as you think!
It is really hard and it's something I worry about a lot. For me I think it seems like I'm struggling along in life but if my T forgets about me then I cease to exist to the one person who is supporting me through all my struggles. It is a tough relationship!