I would have your injector examine you to determine if these wrinkles would be something that resurfacing (i.e. laser or chemical peel) would help with or whether the filler itself is associated with the wrinkles. Sometimes, the product may be placed too superficial and can worsen the appearance of some wrinkles.
Fine lines around the eyes can best be treated with Botox but fine lines under the eyes may need laser therapy. I have been very happy with the Ematrix for the area under the eyes. Ematrix has a special tip for under the eye area. After three treatments with little down time, the delicate skin under the eye area can be restored. Ematrix can also be used with every skin type.
In my opinion, fillers can help with undereye hollows but not as much for superficial wrinkling. This might be benefited by laser resurfacing in properly trained hands. Good luck.