Yes!!!!!! Absolutely! 100%! The skin around the eyes is more fragile than the rest of the face. It is more prone to dryness, irritation, and is much more sensitive. Using your facial products too close to the eyes can cause irritation so invest in a proper eye cream.
Eye creams are especially formulated for the delicate eye area and can help with dryness, fine lines, puffiness, dark circles and to tighten the skin around the upper eye lid. Make sure you apply sparingly and gently and tab it on your upper and lower lids when ever you cleanse your face.
My personal favorite eye cream is Dermalogica's multivitamin power firm. You can also dab it on your lips to keep them moist. The ingredients include Antioxidant vitamins C and E to help improve elasticity and scavenge free radicals while shielding vulnerable skin by acting as a barrier against further assault. It makes my eyes look so bright!
Eye Crean also makes a great make up prep prior to concealer application. Make sure to get a product formulated without artificial fragrances, colors and parapets.