No reverse

Pleas help. I know a bit on working on vehicles but this issue I'm having I have never heard of so I own the truck listed above lifted. With a high out put 5.0 motor and when I got the truck the automatic shifter broke so I been reaching under the dash to shift it. Well one day I'm doing bout 50 mph I realize I was in second not drive so I went to shift it but accidentally put it in reverse well the tires locked up and truck came to a screeching halt. I quickly put it back in drive because traffic behind me and it drove just fine like nothing happen until I got home. I went to back in my driveway the reverse light came on but truck would not back up so I thought I stripped the gear. So I got out and tried to push it it would not budge. Tried it in neutral still would not move. So I shut off truck. Finally I could push it backwards but only if the truck is off will it go backwards but went it running it wont budge even with 5 people trying to push it. Did I some how lock the reverse? But if so why only when the truck is off? Please help. I know the transmission can't be bad it only has 139,000 miles on it and it drives great still in for word.

Please help

Mikey