Other than the skin issues, is your dog healthy? Is your dog getting prednisone or some medication to make her uncomfortable?
Don't have much to say about the dog park, they just don't work for some dogs. My dogs have never shared the water bowl. Also since you were in the park first and alone, your dog may have felt protective/possessive of it. The younger dog may have shown bad puppy manners that your adult does not wish to tolerate anymore.
As for the barking, it almost sounds like she is trying to say "hello", get attention. My female is very vocal. Often if someone wants to meet her, I'll ask her if she wants to say "hello" and she barks, it is her greeting. Scary to people who don't know her. If I were you, I'd look into some group dog training classes so you can learn some skills on how to get the dog focus on you, ignore the other people and dogs, "leave it". I think being around other dogs in the class will give you the opportunity to desensitize her to being so stimulated and maybe fearful around other people and dogs.
Once you and your dog learn some strategies for dealing with the barking and reactions, then see if there is a dog hiking/walking group in your area. My dog learned good behavior from being around (hiking and walking) other well behaved dogs. When the dogs are into their smells and moving forward they tend not to be so focused on each other and seem less aggressive.