C172 pilot reported a loss of aircraft control on takeoff resulted in near contact with airport signage and a difficult climb out of the airport environment.

Narrative

This C172 is equipped with continuous flap adjustment rather than detents; and also has an airspeed indicator that indicates MPH rather than knots. During takeoff phase of touch-and-go on Runway XX; the aircraft started to drift to the left of centerline as I applied full power. I applied right rudder to stop the drift; but the leftward drift became worse. I applied light right brake as an additional effort to stop the drift; but again this did not work. Now being very close to the edge of the runway and at about 60mph; I attempted to get the aircraft airborne. The airplane barely became airborne (probably 1-2 feet in the air) as I passed the left edge of the runway. I looked to my left reflexively to check flaps at this time; and I noticed they were still in the full down position. I immediately retracted flaps slightly to try to gain speed and start a climb without touching down again. My indicated airspeed at this point was less than 40 mph. The flight path of the aircraft was probably about 20-30 degrees to the left of runway centerline and nearly brought the airplane in contact with runway lighting and signage. As the aircraft started to slowly climb and accelerate; I retracted flaps in small increments until I was at approximately Vx (70 mph.) I attempted to climb out at about 70 mph while turning back toward the runway centerline. During the initial climb out I came very close to the tree line south of the runway. The rest of climb-out was uneventful and I proceeded back to my home airport without incident. Testing brakes and steering after touchdown and visually inspecting wheel pants; wheels; tires; and brakes; after landing revealed no issues. I believe the initial left turn and loss of control was a result of inadvertently not retracting flaps prior to applying full power during touch and go.