Slipping in OD?

[Lumina3.1]

I have a 93 Lumina Euro 3.1L 4-speed auto. I have a very noticable steering wheel shimmy from about 55-65MPH. IF I down shift into 3rd gear from OD, the shimmy will stop. A friend of mine told me the tranny could be slipping in OD. How can I check and see if that is the problem?

[93CutlassSupreme]

if the trans was slipping wouldn't the engine be revving up while the speed stayed the same, or fell?