Dog barking when other dogs fight or bark

Hello, I have an almost 5 month old border collie pup. She is super friendly with humans and dogs but can get a little shy/submissive when the dogs are bigger/bulkier than her. Her energy needs are being met through mental stimulation – she is too young to run as much as an adult border collie but does get some exercise throughout the day.

There's a very good dog park nearby where most of the dogs are super friendly which we take her to. Every now and then, some of the dogs will get into a little fight but usually sort themselves out within 5 seconds. (I've been going since her vaccinations were sorted and I've only ever seen 2 fights) My dog is usually with me, on lead away from most of the dogs.

My dog is relatively well trained and calm but high distractions are a little tricky (Usually things that get her energy up) When we walk her, there's a house that has dogs that bark and that's when she started her barking back. I usually try to distract her when we walk past and reward her when she ignores them.

We went to the park and everything was normal. She greeted the other dogs, sat with the people a bit. A Dachshund puppy arrived and it's one of her favorite dogs to see so her excitement started to increase. Every few minutes, I would get my dog to come with me a little further away from the dogs and I'd get her to sit so she could calm down a little. (She doesn't listen when her excitement is too high which is why I do this). While her excitement was up, 2 dogs a bit away from us started fighting but it was resolved quickly. She wouldn't stop barking though and trying to pull to go to where the fight was. She wouldn't listen to me when I called her and I had to pick her up and take her a few steps further away so she would calm down.

What I need advice on: Basically, I just don't want her to become reactive if she sees dogs. She is super friendly with dogs and people but she reacts when other dogs react. Is there anything else that I should be doing during these situations besides picking her up and taking her somewhere else to calm down? I am worried that human touch will be seen as a reward as she is very comfortable being picked up and loves pets/affection.