once you can punch correctly you do shadow boxing to practice foot movement and putting you punches together or leaning weaving slipping and such things stringing your skills together, it might help you fine tune your style, its best done in an open space with a big mirror, like in my gym, the walls are mirrors and it rocks for shadow.
also you might think it feels uncomfortable doing shadow boxing whther at home or in front of others at the gym but its worth doing and normal to do so keep at it and it'll help alot.