Sorry you are having trouble! If your child cannot take the PSAT but you feel that they would score well, another option to consider is “Alternate Entry.” Here’s a recent thread that discusses this option: PSAT 2022 Test centers
Edited to add: I just noticed that your kid is in 10th grade. I don’t know what to suggest in that case. Our school district doesn’t offer the PSAT at all to sophomores, no exceptions. Even for juniors, our school only has enough capacity for half of the junior class, and if more students want to take it, the seats are distributed by lottery. Good luck!