Restylane under the Eyes
From your description I am not sure if the eye itself or the area under the eye area is red from the injection. You can be allergic to Restylane but it should not affect the eye itself. I would consult with an ophthalmologist if the redness persists. I usually prefer Belotero to Restylane for the delicate under eye area. It is important to find a board certified dermatologist with a great deal of experience in cosmetic Dermatology for the best results.
Alternative to Restylane in the tear trough
Restylane should not have an effect on the actual eye itself. Like some of the other physicians I have seen some intermittent swelling of the skin around the eyes after filler in the tear troughs. If you would like to try a different product there next time, I have used Juvederm Ultra in the tear troughs. Make sure you are with a board certified physician and experienced injector. If your swelling continues, you can have the Restylane removed as it is a hyaluronic acid filler and can be dissolved with hyaluronidase.
It is rare but possible to have a reaction to Restylane.
It is a rare occurrence, however I have seen a very few patients who have had immediate swelling that lasted for less than a week and then went away. A small amount of swelling is common and not considered to be a bad reaction to Restylane.
Restylane in tear troughs
Occasionally, I have heard of women with periodic swelling in the areas of filler placement that coincides with menstrual cycles. Outside of this, sometimes swelling occurs because of impaired drainage due to the filler pressing on lymphatics. To help clarify if symptoms are due to product, Restylane can be dissolved with hyaluronidase. I also use Belotero in the tear troughs, but I avoid Juvederm in this area.