I hate looking like a 13 year old I'm 16 :( what can I do?

ok im 16 but I look like in 13. I'm short maybe around 5.3 or 5.4 ft tall my goal height would be 5.9 is that tall?. I don't think I have had my growth spurt my dad side of the family are tall, mom side kinda short. I weight 105 lbs. i actually weighted 95 lbs but i started eating a lot more idk why. isn't puberty suppose to make you look more of a man like bigger muscles and other stuff? I started going to the gym and working about a week.