Skin above cleavage oily and breaking out for months after breast implants. Is it related to surgery?

Would have loved to see a posted photo! Either way you need in person term consult to determine the issue you are having... 

I would consider some degree of irritation of the skin after surgery.  Sometimes when the skin is tight it can be very shinny but not oily.  If it persists see your plastic surgeon.  

In our practice we have seen a few similar patients. Although one can never be sure of the cause, some patients felt it was due to the velcro band (bandeau) that they wore right after surgery. In all cases the issue resolved without treatment.  Ask your surgeon directly. He/she may have experience and can give you the best answers.  Best, Below is a fully healed breast augmentation on a patient who wanted very natural breasts.