You should really use 'still' because we use this word for situations which continue - and age continues to increase. We use 'yet' in negative sentences, so you could construct a similar sentence communicating a similar idea with 'yet' - like "You are not old enough yet." https://dictionary.cambridge.org/grammar/british-grammar/already-still-or-yet

I'm not pretty sure, but when I speak to people usually I heard that sentence ''You're still too young''. I'm sure you're looking main meaning but my knowledge not enough yet.