Can i still get good at violin at 14?

I started violin when i was 12 with a private teacher because i assume they don't let anyone in music school if they're over 10 because my fellow friend tried to join when he was 9-10 and they told him that he was too old but still managed to get into there so there was literally no way i could get there at 12. I'm now probably at 2nd(?) Music school grade level and play 1-2 hours a day and the main question here is will i ever be good enough to get into some music school and play publically because it's depressing to only play for yourself and you basically get no motivation to practice because you won't perform for nobody(if you're saying you can perform for your family 1. It's not the same 2. My family doesn't want to hear me playing and they're usually annoyed when i even practice).