Don't feel bad. You're not alone. My dog barked like crazy when I took her to the doggie park in the beginning. It was embarrassing, but if the people around you know anything about dogs they will forgive you

I guess you allready know you should never pick the dog up, you're just teaching him that it really is something to be afraid of. And of course there isn't

I had to take tiny steps with my nervous little girl. We sat down at a safe distance from the other dogs. Every time she looked at the other dogs without growling she got a treat and some praise. We moved a little bit closer every day. Sometimes we had to take a step back, but all in all she became safer

If you know someone who has a dog who is good with other dogs, bring that dog along so your dog can see how comfortable that dog is with the situation.
We kept our distance for the first week, playing on our own. After that we could walk into the midst of 20 strange dogs without a problem.
I made sure to never pick her up or comfort her. If she did get scared, I let her hide between my legs, but I did not reach down or comfort her. She needed to learn that she could manage fine without my help. If she got overwhelmed and started barking. I put the lead on and guided her away without a fuss. But I never went straight home, I let her off the lead when she calmed down. That way we would always come home with happy thoughts about the dog park

If you are familiar with the calming signals, use them! You may look like an idiot, but it is really effective!
And remember to stay calm and confident even if you don't feel that way. The dog pics up on your mood and will reflect it.
Maybe this is old news to you, but I have struggled a lot to learn how to make my nervous dog confident

so I figured I'd write my own experiences in case they were helpful. I would also recommend the books "Help for your fearful dog" by Nicole Wilde and the calming signals book by Turid Rugaas if you have not read them. They helped me so much with my little girl!