First things first. You can't have a free armswing if your ball doesn't fit correctly.
Second thing second. You will not be able to be a good judge of what a correct fit is. As a former pro shop operator, I can not tell you how many people would come into me, show me how someone had butchered their grip, and tell me "Yeah, it fits awesome!" while I looked on horrified.
Do you have a good pro shop in the area in which you live? If you don't know of one, you could state the area you live in, and someone here could help find you a good shop near by to have your grip checked.
After that, then the suggestions would be helpful. If you actually HAVE to squeeze because of bad ball fit, all of the suggestions will be for naught, and you will want to quit even more.
Get your fit checked, and then the swing can be addressed.