I would be interested to know what flavor cosmetic surgeon you saw.
Having said that, some cosmetic surgeons have the "big cutter' mentality: every thing needs to be done with the knife. You do have a tiny amount of lower eyelid fullness that is the results of orbital fat. This is what is addressed with lower eyelid surgery. A more sophisticated approach conserves this fat and moves in into the top of the cheek as a living graft. This is called an arcus marginalis release. However, your lower eyelid fullness is small and your tear trough hollow is large, so the benefit you will get from this procedure will be modest.
Filling your lower eyelid with Restylane is a non-surgical treatment that will likely help you for more than a year, perhaps two years. You need about three 1 milliliter syringes of Restylane (1.5 on each side). In my West Los Angeles office that service would cost you about what you were quoted for surgery. I suspect that in Ohio, you are likely to get that filler service for much less than the West Los Angeles price.
I think fat grafts and other permanent fillers are a big mistake for the lower eyelid.
In Ohio, I can recommend Jill Foster, M.D., without reservation. She is an oculoplastic surgeon in Columbus. She does both eyelid surgery and periocular filler treatments. Additional eye plastic surgeons in your area can be found at the website for the American Society for Ophthalmic Plastic and Reconstructive Surgery: www.ASOPRS.org.