The contraceptive implant Implanon is a progesterone based contraceptive that inhibits ovulation for up to three years as long as the implant stays in the body. With the withdrawal of a concentration of progesterone it is not unreasonable to consider that a hormonal imbalance may occur post removal.
Cystic acne in the jawline and around the mouth is usually considered to hormonal in origin.
Hormonal balance can be treated successfully with the use of herbs and nutrients however I would suggest that you consider visiting a Naturopath who can assess your individual case. I prefer not to give hormonal advice in general terms as there are so many variants that have to be considered as the cycle changes with hormonal peaks and falls throughout the month.
Consulting a naturopath will allow the naturopath to establish your cycle rhythm, any problems with hormonal regulation and investigate any other symptoms you may experience.
The use of a hormonal implant whilst effective is not without documented side effects and some of these and the implants residual effects on the liver can be addressed by your Naturopath too.