Hiya Liz!
And welcome to BAF! It's a really warm and friendly place so feel welcome to share your feelings, or maybe even come to a meet if you feel able when you're in Brighton.
I must say I recognise a lot of myself in how you describe being friendly with people on first meeting, but then getting anxious about meeting again, and then following a pattern of avoidance. I'm learning how to break this pattern at the moment by trying to change my behaviour in this regard, of course altering intrenched ways of coping takes time, but i'm learning to be patience with myself and allowing things to happen slowly. For me going to BAF meetings, and generally trying to socialise more than i've done for a longtime is part of the way of changing. When I went to the first meet I felt really quite anxious, and typically I might of avoided going again, but this time I set myself the small goal of going to meets regardless of anxiety and i'm finding that for me it's helping to build up my social confidence, and now i'm even thinking about going to a few evening classes in September to help myself further.
Like you I'm quite new to Brighton, I moved here in January, it took me ages to find a flat during the winter and of course any kind of move is hugely stressful, I did eventually find somewhere, as I'm sure will and this is a great city, with loads to offer and a very laid back vibe and it's very excepting of different kinds of lifestyles, so maybe being here will also help with your confidence as I feel it is doing for me!
Lot's of luck with everything! And hi to you also Cyclegirl!
L