Yes and yes are the simpel answers.
I would suggest (without having examined you) that you lack control of the thoracic vertebrae you describe. By loading up the weights, you are compressing those joints in particular. By "wiggling", you free those joints up but they aren't going to like it for long.
Which city are you from and perhaps i can suggest some physios that have been trained properly in the thorax to help. I can guarantee that 99% of physios don't understand the thorax properly. Otherwise just email me.
Cheers
P.S. Don't let anyone "crack" your back down there because it is NOT more mobility you need there but CONTROL.