welcome to the forum. There is something you can try to do first. Check your bag to see if it has a little loop on the bottom of the bag. Many do, and this loop is used to bungee the bag to the ground to prevent wild swinging of the bag. You could go that route first and see if that works for you.
If not, than yes a heavier bag should do nicely for you. I would recommend a 135lb for your size. It wont swing nearly as much as long as your not "pushing" your punches.
Member of BoxingForum Member H.O.F. (Nov 2007)
Pick your prospect: Henry "hank" Lundy