Hi nrmpl.
Regarding whether you can get into a top 15 school with your current score, your quant score is likely not high enough for that purpose.
That said, you can certainly score 700+ with a much higher quant score. You just have to make the right moves.
Since the test itself seems to be an issue for you, taking more practice tests is likely part of your solution, and there are third-party practice tests with quant sections that are quite good. So, you could take third-party practice tests, see how you do, and work on weak areas as indicated by those practice tests.
Also, probably, you should wait to take the real GMAT again until you have hit your quant score goal, or come close, on a couple practice tests. Otherwise, you could end up using up your GMAT attempts without achieving your score goal.
So, to sum up, you could start by taking a fresh practice test, see what it indicates, work on topics as indicated by that practice test, and then take another practice test. Repeat until it's totally clear that you're ready for the GMAT, and then take the GMAT again.