During a touch and go (C150) should I first raise flaps or set full throttle?
Flaps in a C150 (and pretty much any type) take a few seconds to move. Throttle change is more-or-less instantaneous. If you were to throttle up first, and then change the flap position there is a good chance that you are lifting off while the position of your flaps are changing. This is not a good idea, changing the amount of lift generated by the wings in this crucial stage of flight can lead to a take off stall. You could (and probably will) be too low to recover.

To minimise the chance of this happening, I would say that on touchdown, one of the first things I would do is to set flaps for takeoff ( giving the actuators a second or two to change flap position) before immediately setting take off throttle.

So, yes, your instructor was right. They usually are. In your specific case, I suspect that as soon as you floated too far down the runway, you should have initiated a go-around before touching down. You did not leave yourself enough runway to safely perform a touch-and-go. You dont assess take off distance available once you touch down, you asses it while still flying - you had ~10 seconds to make that call (approach, float, oh shit, go around!)