EMB-145 First Officer reported pitch trim failure on climb resulted in expeditious return to departure airport.

Narrative

Departed late due to catering truck attempting to load the wrong aircraft at the wrong gate. Aircraft was confirmed to be without ice during preflight inspection. Pitch trim test on ground successful; both sides: Captain and First Officer.The takeoff roll was uneventful. Rotation was conducted at the correct speed. I attempted to trim Immediately after Takeoff ON XXL prior to 160 kts. Trim did not respond. Control forces on the control column increased with airspeed. Captain asked; 'Are you ok?' I stated; 'trim is not responding.' I then tried pushing-and-holding the pitch trim rather than using the typical short-burst method. The aural annunciator 'trim' sounded yet nothing was actuating. At that point; 'PITCH TRIM MAIN INOP' appeared on the EICAS. Almost immediately thereafter; we entered icing conditions during the climb. The Captain stated that the priority was the flight controls and we would deal with the icing later. At approximately 1200 feet MSL; He announced 'my controls' upon which we initiated a gentle transfer of controls so that I would release the pressure while he was accepting the pressure of the control column.He immediately stated 'I have the radios; you run the QRH.' The QRH led us to:Pitch Trim Main Sys Cutout ............ PUSH OUTAutopilot ........................................ DISENGAGEBack up system can be used to trim the airplaneThe backup pitch trim worked successfully and we were able to maintain control of the aircraft. At no time did we lose control of the aircraft.While the proceeding took place; ATC requested a turn to the north; the captain stated; unable; flight control issue; we would like to continue straight ahead and request an unrestricted climb." Air traffic control stated; "Proceed as requested. Do you require any immediate assistance?"The captain and I discussed this briefly before he responded and both came to the conclusion that the aircraft was under our full control by using the backup systems as they were designed to be used and instructed by the QRH. As such; an emergency declaration and squawk 7700 was not necessary at that particular moment.When it was safe to do so; I sent an ACARS message to the dispatcher and we notified both the passengers and flight attendant that we would be returning to the field.ZZZ approach vectored us around for a landing on XXR. Approach mistakenly stated we would be landing XXL. When I queried the controller; stating the 'ATIS is advertising XXR;' the controller apologized for the error and told us to expect XXR. The FMS was reprogrammed; frequencies were loaded; identification of the localizer verified; and all altitudes were entered and verified. We ran the cruise; descent; approach; and landing checklists. Captain landed on XXR without any further incident.Upon reaching the gate and concluding the parking check; the Captain exited the cockpit to address the passengers face-to-face using the forward flight attendant interphone station.Maintenance was notified; the discrepancy was written into the log; and we were assigned a new aircraft. The flight continued without incident on the new aircraft.Suggestions: The professionalism demonstrated by my fellow crew members was impeccable. This was a textbook example of excellent crew resource management. We remained calm in a high stress situation and worked together as a team to solve this issue."