hello. well... the exact code would be of great help... BUT if the issue happens more-so when cold... i'd have to say the the "most likely" cause would be the O2 sensor heater circuit. it's possible that the heater for the O2 has failed and isn't allowing the sensor to "heat-up" in the required time-frame.
at the dealership... most of the injector failures are after the vehicle has run for 15+ minutes... so i doubt it would give you a "cold start" issue.
IF you could go to Autozone or Advance Auto parts... and have the vehicle re-scanned and get the code... i could have a more definite answer.
hello. yes it is possible for the O2 sensor to cause a rough idle... especially if the sensor is shorted internally. IF shorted it could cause a "feedback" that when sent back to the PCM... could cause many issues.
there is 1 "quick check" you could do to see if it is related to the fuel pressure regulator...(i've had a few of these cause a cold start issue) the regulator is located on the fuel rail on the drivers side of the engine. remove the vacuum line off of the regulator and see if there is any fuel inside the hose. IF there isn't any fuel in the hose... start the truck and let it run for a couple minutes while watching the nipple on the regulator to see if ANY fuel comes out.
please reply with your findings.