Can't reverse. Gears are acting up.
 

Dodge Caravan 2005, 180,000 km; I blew out a tire on the highway and put the spare on. The van shook pretty bad as you can imagine until I was able to pull over on the side of the highway and come to a stop. Then as I went to back into my driveway a few hours later I couldn't reverse. The gear shift moves to reverse but it doesn't engage. I can switch to drive but the van will only move forward for a few seconds. I checked the tranny fluid and levels and they're fine. Oil levels are down a bit but I can't see this causing the issue. I've read that caravan trannies don't like having uneven wheels and that this can cause a problem with the input speed sensor. Ran a diagnostics but no code was displayed even after 3 tries. Engine light does not come on.
Any help would be appreciated.

BTW, I got a new alternator and battery a couple of months ago - not sure if this is relevant.

im no pro with these cars but i do know that with mixed tire sizes it really screws with the trannys on these cars. is that spare tire u put on , the original one that came factory?