I've had an experience like this lately and it _really_ knocked my confidence, more than I thought it could possibly have. I am now going around in a moment's discomfort all the time, but don't consider this to be a problem as going around saved my nose wheel when it happened to me, I expect. I have my PPL and am sure that a bit more unchallenging solo flying will get rid of the jitters.
I know little more than you, I'm sure, having just switched to the 172 after the nice easy 152 and only having a few hours on it, but have thought a bit about things that go wrong. What I understand to be the case is that because the 172 has relatively large wings/control surfaces for the size of 'plane it is, it responds more dramatically to slight misjudgments, especially if there's a crosswind or erratic wind speed/direction. Also, this means that control pressures have to be quite forceful to work (especially on a go-around...
).
The two things that seem guaranteed to create that viscious bouncing are a) as stated, coming in with too much energy; most people I speak to say this straight away and that you should come in as slow as you think is safe and b) flaring too low (or not at all...) in an attempt to stop that interminable float that you can get in these circumstances!
I think you were probably quite lucky to escape with the nosewheel intact, once that pattern of bounces is set up it's really difficult to salvage. Going around and trying again has to be the best option unless there is a really bad obstacle problem. If you want to chat about this, send me a PM, because I too could use any input or advice.