Does an error code P0736 and P0790 ALWAYS mean a new tranny is in order?

The speedometer was showing 20-30mph while in every gear by park. Was taken in to dealer and the codes showed an in/out put sensor was needed, and a generic transmission code. They recommended a trans flush to diagnose further. Not able to afford the dealers pricing I had it taken to a transmission specialist the same day. When there the car threw different codes than at the dealer. Agreeing on one item the in/out put sensor was replaced and two of the three motor mounts (which the dealer did not notice). The codes were P0736, P0790 and P0720. I am being told that I need an entire overhaul of the transmission costing in the range of $3000. Dealer cost close to $5000. Even though I was told the in/out put sensor would stop the jumping of the speedometer (which it did for one day), it still continues and the engines still revs up as if I was going that fast, however the RPM does not move. With that said the tire system showed a warning and showed on my dash it needed to be serviced. That too was looked at and the Pinion Factor was reset. That fixed it at first. The car has been untouched while fighting with Chrysler for any assistance for the last three weeks. As of yesterday, the tire system issue is showing again a problem on the dash. Now I am being told it could be related to the transmission issue as well.
I would of thought if a transmission was "going" I would at least have troubles driving, shifting, ANYTHING obvious to indicate an issue. I do not, just a speedometer showing different speeds in idle and some error codes. Can you tell by what I have tried to explain with those current error codes, is a new transmission really in order? And is that average for a car that is 5yrs old and 88k to have a transmission fail so quickly. I unfortunately, do not have enough resources yet to fix this nor can I trade in and get something else. It has been a great car for me and has not had any issues since I bought it new so I have not brought it in to the dealer for repairs/work, hence why I was denied any assistance from Chrysler as I am not "loyal" to the dealer. "Quick lube" places and brake specialists is what I could pay for at the time they needed to be done. The dealer is and has never been competitive for me to be able to visit them for routine maintenance. Any advice on this matter is greatly appreciated.
Thank you.