Updating software for on board computer OR resolving PO 776, PO 793?

What is your question?

My Camry hesitates when going from 10-20mph, exactly like this previous Repair problem detailed "Hesitation on acceleration of Toyota Camry" I also have PO codes 776 and 793 when the check engine code is checked. Should I take my car to dealer to get update of board computer as suggested (although one dealership says there is no update for my year Camry) OR to an auto shop to get the PO codes resolved?