The PCM doesn't know what size tires are on the truck. Reprogramming the tire size is only to correct the speedometer and the odometer. It won't affect the shifting. Changing to larger tires can't make the TCIL blink. Disconnecting the battery will erase the code, but it won't fix what's wrong. The light will come on again if the problem is still there.
You need to take it to a shop that can read the codes. Most independent shops and all Ford dealers can do it. The auto parts stores that read codes free can't read Ford transmission codes. Don't go there.
Former Ford Automatic Transmission Engineer, 1988-2007