dober_gurl is right on the money. By picking him up he's getting love and affection for bad behavior. The other dog owner was right too, if you're holding him the other dogs don't see you all they see is a rude dog who's lashing out at them. Will you actually get bit? Maybe, knocked down would be more my thought. Most dogs will not actually bite another dog initially, they will correct him/her and let them know that that behavior is not tolerated. This will happen with a bit of growling and maybe even a little teeth, but usually no actual bite wounds. A lot of owners get worked up over a "fight" that really is just a manners lesson.
If you feel uncomfortable around the bigger dogs, your dog knows it. So you have to stay calm. Try some things with him before you take him to the park, maybe see if one of the other dog owners would help you. Have them walk their dog close to yours and when you see that he is about to act out (watch his body language so you catch it before he actually does it), tap him with your foot or leg to distract his attention away and give him a command, "to me" or "attention" whatever. Preferably try this with a dog who is going to ignore him, watch some of the dogs and their owners at the park if you don't of anyone yourself and see if someone will help you. And good for you for trying to stop this behavior!!