I plan on applying to graduate school school soon and I'm confident the rest of my application will be pretty solid. However, I'm worried that a quant score of 160-163 will put me below the other applicants. Most have quant scores of 165+. I could break this, but I have a huge problem of making silly mistakes when under pressure and trying to keep a good pace.
Every school is different in how they view this, but I think the consensus now is that such scores are not as important as they once were. On the other hand, you have a negative piece of information about you, and you want to balance it, or overcome it, with lots of positive pieces of information.
I suspect that most places, with the possible exception of very large programs, take a more wholistic view of their incoming candidates. If your total application package is strong, I wouldn't worry about it, but be prepared to discuss it in an interview.
In fact, exams of that sort favor certain kinds of learners and disfavor others. This is, I hope, fairly widely recognized. The tag on the question suggests you want to study mathematics. Lots of mathematics isn't about "quantity" at all, and requires a different sort of thinking. Spacial, for example, or highly abstract thought.
But knowing that you make silly mistakes under pressure, you might want to find a way to address that directly, though I can't help you there. I assume there are academic counsellors who have the expertise to give you a start on it, at least.
You will find a lot of pressure in grad school, of course. A lot of pressure. You will want to find ways to both lessen it and to deal with it. On the other hand, not everything is like a high-stakes test, so the pressure is of a different sort.
The wisdom (?) of the internet suggests: https://www.thoughtco.com/do-you-have-a-good-gre-score-how-to-tell-1686221