I have what I would call moderate crowd anxiety. I don't totally freak out or go into full fight or flight mode, but I do find myself getting more and more tense as crowds get thicker. Some things that I do in the parks or at crowded events in general include:
1. Find an escape route. Especially at the parks, there's always SOMEWHERE that's less crowded. A little-known pathway, a less popular shop, a former smoking area...as soon as crowds start getting beyond moderate, I start scanning the area to find both a place to go and a route to get there. I rarely need it, but it's comforting to know I can.
2. Plan breaks. I try to plan my schedule in such a way that at least once in the morning and once in the evening, there's time to relax out of the crowd. This can be a visit to a less popular attraction or sitting down with ice cream in one of those less populated areas. Even 10-15 minutes helps me reset.
3. This is a huge one for me, and it works absolutely everywhere I've been. Find an anchor. If you're going to be standing still in a crowded area for a long time, like for fireworks, pick a spot where you can lean against something. A fence, a tree, a lamp post, anything that won't fall over. I've found that just being in physical contact with a solid object helps keep me grounded, with the side effect that you at least know you won't get jostled from that direction.
I hope this helps a little! Crowd anxiety can be the worst!