Oh I am so sorry to read about this. I think your actions just sort of go on auto pilot when things like this happen. So don't be too hard on yourself. Maybe someone here will have some great advice on what you should have done, not to kick you while you're down, but to give you some ideas if something like this should happen again. Dogparks, at least the ones I've been to, vary greatly, but I'm not a big fan of them. Of course that's easy for me to say because I have several acres for my pups. But I have used them when DH and I were living in an RV with 3 dogs (2 adult basenjis and a lab). I'd rather had access to a private yard, but that just wasn't available to me. (well there was a place for me to do some agility but that was an hour's drive, so not practicle for regular exercise.) And so, we all try to do what we feel is best for our pups.
I would put in a police report on the GSD. There needs to be a record of what has happened because I think it will happen again. I'd bet this dog has a history of this type of behavior and it's unfortunate if it has not been reported before.
There is no doubt that you love Giz, be kind to yourself too. Aloff's book on dog language is a great book to add to your collection. AND I'd suggest getting a copy of Control Unleashed. The author's dog, Snap, had real issues with other dogs and she was able to help him overcome it. The Look At That game is so helpful for dogs that are nervous about something. Who could blame Giz if he decides all dogs are now out to get him. Poor boy. Do you have a good chiropractor vet? I think that would be helpful after some of the swelling goes down. I like arnica (homeopathic) for this sort of thing.
Take a few deep breaths. It's over with now although the adrenaline rush may take some time to come down from, but it's over with and you are okay. Gizmo will be okay.