How Can I Get Rid of Cheek Bags?

It would be helpful here to see some photos.  Very difficult to give you guidance if we cant seeing what we are addressing.  It does sound like you need some volume perhaps.  We also need to know how old are you.

Judging by your description it seems as though you are suffering from malar festoons.
The treatment of malar festoons usually requires volume replacemend in the cheeks, a cheeklift (our version is usually the USIC or LUSIC cheeklift, ultrashort incision cheeklifts). For graft material, we prefer LiveFill for volume augmentation.
Even with these treatments, the surgery is not typically curative, but does typically give a great deal of improvement.
Occasionally, it is possible as a second stage to remove directly the bags with an incision on the cheeks themselves.
Needless to say, the cheek area is extemely delicate. The lower eyelid must always enter into the equation; pulling down of the lower eyelid must be minimized by clever design of the surgery.

The cheek bags that you are describing sound like festoons and are a very difficult problem to get rid of. If large enough, they can be removed through a direct excision. A facelift will only minimally help them. A cheek implant will not help them at all. Make sure that you are taking a low-salt diet so as not to have fluid retention in the cheeks, make sure that all nasal allergies are addressed. Cortisone shots have been attempted in this area; however, give only temporary results.