Hi welcome to HCM
Dear , your gesture of joining gym is very wise . You already have good height . No harm increasing more if possible . upto 22 . You can try increase ht.
For your age your weight is little more which you should consider with the advice of your instructor .
No amount of exercise , except,
Yoga Postures and a proper balanced diet , will cause your bones to lengthen, but stretching strengthening exercises can improve your posture so you stand up straighter and help grow taller .
Using the equipment at the gym to stretch your spine and correct poor posture will combat habits that lead to slouching .
Increase your height with exercise at the gym.
Strengthening the lower abdominals supports your spine and helps you stand up straighter.
Every gym has some kind of pull-up bar or hanging station. Simply hang from this bar.
Hanging lets gravity gently pull and lengthen your spine, increasing the distance between your vertebrae. This is a simple way to stretch your arms, back and even your legs. Hang and stretch for 20 seconds. If possible, use a bar that lets your entire body hang with your legs straight.
It will surely help to achieve your goal
Consult a fitness professional at the gym on how to stretch your trouble spots.
Hope this helps solves your query .Take care .All the best .Get well soon
Don't hesitate to come back in case of any further query .