Is it possible to increase my score this much on the PSAT?

Definitely, I never took a PSAT cl, but I did for the ACT cl. I had a composite score of 27 and the ACT prep cl and the study materials I bought at Barnes and Nobles boosted my score up 4 points. You should give studying a try for the PSAT, it will pay off and it will boost your score. Good luck!