It sounds like you have malar bags or pouches.  Typically when people talk about "bags" they are either talking about lower lid fat bags which true fat pockets pushing up against the thin orbital septum and eyelid skin (fat pseudoherniation) or they are talking about malar bags, which are areas of edema or fluid retention cause by a triangular zone of ligaments on the upper cheeks.  

True eyelid bags are treated with fat excision or fat re-draping alone or combined with skin excision (muscle can be removed too).  

Malar pouches are very tough to correct and there is no standard solution.  An extended lower lid blepharoplasty does help many patients but there is no guarantee it wont make it worse.  Injections of fillers around the malar pouches can help smooth and camouflage the pouches.  However, any irritation, be it lasers, chemical peels or aggressive injections of fillers can make the fluid retention or edema worse.  

See a few doctors and see what they would recommend in your particular case.