Hi
I had a similar issue, where the resolution of the eyes was just too low.
They looked just liked your eyes, very pixelated and not smooth.
I noticed that my simplify brush (or any other) does not add new resolution to the mesh.
I ended up moving to object mode, adding decimate modifier 50% and when I went back to sculpt mode I was able to add new resolution to the mesh and create eyes that are as smooth as the one on the tutorials.
Not sure how I ended up in this situation, this is the second time I am trying out these lessons, first time round had no issue with the mesh (a part for the fact it looked awful lol)
Avi
