Your description of wallowing side to side on final is terrifying - I would have rammed the power in and gone around like everyone else says. I made a complete arse of my first approach on first solo flight, forgot to trim back with flaps on base leg, was way too high on final, forgot CRAP check to put carb heat back to cold etc etc etc did a go around - second approach and landing was great as a result, and with go aorunds you get to fly a bit longer too! I'm 30 hour student