She may have had a nasty experience in a dog park previously, she may have been badly bashed by other dogs.
Please stop taking her to the dog park, she is telling you she doesn't want to be there and eventually other dogs will pick up on her fear and insecurity and attack her.
As someone previously said GSDs are not very social and prefer the company of their own pack. She would be much happier with going for a walk with you as exercise, she doesn't need the company of strange dogs plus she won't be getting any exercise at the park.
There is not need to take her into a dog park.
if your GSD is eating and eating and eating and losing weight - please consider testing for EPI.
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