It just all seemed a bit dramatic at the time.
For a low-hours student, I can imagine that a GA can be very dramatic. Especially if it's not due to your own fault but because of external circumstances and ordered by ATC. Just keep your head cool, acknowledge the instruction, put full power on, carb heat off, keep the nose fairly low so you build speed first without losing any more altitude, get rid of some flap if you have to and then climb away. And yes, this can happen even at 1 ft. over the runway.
ATC told me to continue my approach at 500 feet
Just so I understand this correctly. Did ATC call "continue approach" when you happened to be at 500 feet, or did ATC call "maintain 500 feet" when you were on final approach?
I guess it would have been the first, and this is quite normal. You've called final, you had probably had confirmation earlier on that you were first to land (except for the one one the runway) and this is just ATCs way of saying "continue your approach as if you're going to land but I can't give you a landing clearance yet because of other traffic on the runway. But I think the timing will work out and I'll be able to give you a landing clearance in due time". So just continue your approach as if you're going to land, but just make sure your wheels don't touch the tarmac yet.
I fly from a long runway with exits at the beginning and end only and we get this a lot: traffic unfamiliar with the runway exit layout touching down at the "big aircraft" touchdown point, and then taxiing all the way down the runway. The trick is then to continue the approach, initiate the flare with a bit of power on so that you float indefinitely without touching the tarmac, and chop the power as soon as you get the landing clearance. Only when the landing clearance doesn't come when we've floated halfway down the runway (or more) do we initiate a go-around. Which is actually quite tricky when you're so close to the ground, due to the torque effect and everything. Increase power carefully and keep the nose pointed exactly where it was until you've got full power on. Only then raise the flaps carefully and climb away.
Come to think of it, this might be a very good exercise to do with your instructor, sometime. Don't do it with a stiff crosswind though, at least not the first few times.
Oh yeah, and anytime you do an approach and end up below 500 feet (I think) you have to pay a landing fee. Doesn't matter whether you call it a missed approach, go around, touch and go or full stop.