I think the opposite is more likely to happen. When boys were castrated before puberty, they grew taller than average because testosterone helps fuse the growth plates that allows you to continue to grow.
Growth plates fuse with you stop growing. Perhaps you can check with a specialist doctor to see if yours have already fused?
The minor difference here is that you're only lowering the effects of 5-a Reductase with finasteride. In order for this to stunt your growth, testosterone would have to be the thing that helps fuse the plates and the effects of 5-a Reductase what slows it down, but that seems far fetched.
According to this site that helps parents of children who have a 5-a Reductase deficiency, parents should be warned of possibly lowing final adult height with added male hormones.
https://ghr.nlm.nih.gov/condition/5-alpha-reductase-deficiency
"If testosterone is used in a prepubertal patient for a prolonged course of therapy, parents should be counseled over the potential to decrease final adult height secondary to androgen associated skeletal advancement"
If I were in your situation, I would take finasteride, but you have to make your own decision so you can't blame anyone.