Will not shift into overdrive

Check for trouble codes related to the transmission. If it refuses to shift to overdrive, there should be a code to direct you to the problem. As far as the alternator, I would make sure that it is the same as came with the vehicle. However, unless it is really under powered, it should not cause this problem.

The alternator that was put in came off a 4.6L. Will that make a difference?

Nope.

Disconnecting the battery will reset the transmission controller and could make it not shift until the truck re-learns the shifting patterns. Normally on a Ford you can disconnect the battery, let it set for about twenty minutes to discharge the memory. Now start it and let it idle with everything off until it gets up to operating temperature. Now turn on the AC and drive it normally for five miles or so. Turn off the AC and see if it has regained overdrive.

Thanks, I will try this and let you know.