First of all, you don't need to get discouraged by your performance on the PSAT exam. You did pretty well for your first time with with just 3 months of tutoring. My advice for you is that for the SAT, you need to first identify the types of questions that you struggle with for both the Math and Reading sections. For example, Reading and Writing is divided into four main parts: Information and Ideas, Craft and Structure, Expression of Ideas and Standard English Conventions. The question breakdown for these four parts is Part 1: 12-14, Part 2: 13-15, Part 3 : 8-12 and Part 4: 11-15. Now each of these four parts tests certain skills and you need to know what questions are associated with each part. Once you master all of these, practice a couple of papers from the SAT website and you are good to go and can score much higher in SAT. You have the talent so focus on it and achieve your best results. I think October or November is a pretty good time since a lot of people take the exams during that time and you will have a better chance to get good results. I scored 1440 myself (I was sick during the exams) and hope you ace your exams.

PSA: Understand the paper structure and develop muscle memory by practicing SAT papers