Exercise! - I need a FULL BODY sports bra!

I've been jogging and doing the elliptical and stair stepper for a while now and am trying to transition to real running. Cardio wise I feel up to it but I feel like my butt/thigh area and stomach just move an absurd amount. It becomes quite uncomfortable... I've tried compression shorts but that doesn't help my loose stomach. I have lots of extra skin on my stomach and back of my thigh area... One day I wore those all over compression type things that you'd wear under a dress but it was miserably itchy after I started to sweat.

Does anyone have similar problems? Have any solutions to offer?

I have felt that heavy jiggling--more than jiggling, more like thuding? in my butt/hip area. I also find it uncomfortable, so I don't run. I walk fast and at an incline on the treadmill. Maybe when I lose more weight, I will keep attempting to break into a run and see how it goes.
I had wondered about compression shorts.
My only advice would be to not run, but keep at it in other ways. Maybe do a consult with a personal trainer for ideas of more challenging work outs that would be comfortable.