what should i do ..

so ive been on depo for about 3 months and due for another shot this month. i like it and want to continue it but im kinda stuck between going through with it and not going through with it because obviously im aware of the fact ill grow unwanted hair and mine so happens to be on my lip.. sometimes i feel like i walk around with a constant 5 o'clock shadow, is there a good way for me to get rid of the hair from growing so fast or at least containing the shadow? while continuing the shot? thoughts and suggestions..