Don't count on it. My dad was 6'1", my mom was 5'7", and everyone had me pegged for at least 6'2". I never cleared 5'11 and 3/4". I pretty much reached my adult height at 16.

My legs are as long as yours, and my arms are long, and my riding posture is Eddy-ish, so I'd be on a Large with a 12 cm stem. At 6'2" (188 cm) I'd put you on a Large. At 6'4 (193 cm), you'd be right in the pocket for XL. XXL would be a mistake unless you shoot past 6'5". Anyway, you'd have a hard time controlling it at your current height.

This is a little off-topic, but while you're still growing you might want to consider a bike that is more easily customizable in the cockpit department. You're likely to be swapping stems and handlebars as you grow and gain skill and experience.