your eye still looks quite flat. if you use two meshes, one for the “inner” surface (white eyeball, iris & pupil pulled back a little - as described in the tutorial) and one for the outer, glossy surface, including the bulged lens thing would wokr out much better. this way you could also turn on reflections for the outer material only, and i believe that would look much better than now.
sorry to say that, but the part of the face that is visible still doesn’t look like a part of the face. as the human eye/brain is extremely sensitive to even small details, the image automatically looks “unrealistic”, regardless of the lighting.
so i’d concentrate on the geometry first, and then try to find the best lighting solution.
do you have a camera? if yes, make a close-up shot of your face, preferably using daylight. or in a room with very good (bright) light.
then zoom into the area of interest and watch, watch, watch. try to find out where the shadowed/bright areas are, what the eye is actually reflecting (you can exaggerate that later, of course) and so on. a good reference will help you a lot to find the “weak” areas.