Transmission not shifting properly due to underbody damage

After backing out of an icy, snow-covered driveway, and tearing up the underbody, the engine light started flashing and giving a code for a glow relay (which I'm aware is only relevant on diesel engines). The car accelerates normally through 1st and sometimes 2nd okay with occasional jolts, but when trying to go into 3rd the car jolts and loses the ability to accelerate, tries to jump to 4th, jolts again and will either go to 5th, or go back to 2nd depending on my speed. Sometimes in automatic mode it will catch fourth with little power but other times it will not. In manual slapshift mode I have no power whatsoever in 3rd or 4th. I was told I had a bent radiator support and other things possibly bent underneath. That is the extent of my knowledge of the problem.