Dear lad68,
I like to think of Botox as something that is used for dynamic lines or lines that are obvious when you are moving a particular muscle on the face. On the other hand, fillers (such as Restylane, Juvederm, fat, etc.) are used on static lines/folds or lines that are present even when you are not moving parts of your face.
Around the eyes, Botox is usually only used to reduce the appearance of “Crow’s Feet” which are the lines of movement that you see by the side of your eyes when you smile. Botox would not help reduce the appearance of bags.
A filler, such as Restylane or fat, may be placed along the area where there may be under-eye hollows or dark circles. However, you should go to a highly experienced injector when getting this area filled because this is an area that is not forgiving of improperly placed filler.
Bags under the eye are often caused by fat protrusion and if this is truly the case with you, then the only option would be surgery to reposition or remove the fat through a blepharoplasty procedure. Sometimes what a patient views as “bags” is really not a protrusion, and the surrounding area can be injected with filler to conceal the appearance of bags. Without photos, it is difficult to say which one is your issue. I would recommend you have a consultation with someone who has experience with fillers and surgery, so that he/she can guide you appropriately.
Dr.Sunder