Eating protein in the adolescent years is important.
I thought so too, but my son, who will be 16 in a few weeks, is following precisely the same growth schedule I did, and is now over 5'11", despite becoming a vegetarian over a year ago and refusing to eat high-protein foods like beans and peanut butter. His feet are already as big as mine (I'm 6' 2 1/4").
His mother is under 5' 2", so if he gets taller than me it won't be because of genetics.
If your nutrition is "good enough", you will follow your preprogrammed genetic schedule -- even a diet relatively low in protein is "good enough" today, when food is so abundant. The main thing is to avoid any period of deprivation while growing up.
Supplements won't really help. If you want to get taller than you are genetically programmed for, you will have to eat huge amounts and get fat too, or else exercise in an extremely rigorous way, and even those steps will only give you an inch or two.
Size does matter....eat meat!!
Calcium (most likely from dairy) is even more important for bone growth, the single most important requirement for height.