I like to chew on my food and wad it up in my mouth so I can pick out the food later.
Have you ever discuss this with someone?
I'm kind of embarrassed to admit it to other people what I am like.
There is a wide variety between cultures concerning acceptable behavior. Eating in the manner you described is quite unusual, and you can expect most people to not have a pleasant reaction. You should explore what's behind this behavior and try to correct it -- at least when you're eating with others.
I do it when I'm in a group of people.
I think that could be something you could work on when you are out in public. People do not like to dine with people that have bad table manners. You could try to stop it a little bit at a time so it doesn't affect your social life.