That's the thing with working on leather carvings for the first time and not getting the proper instruction to help you advance.
I'm just as new to carving and my experience is the same, don't expect to get it right the first time.
That eye has a lot of surface area and appears flat because the leather is flat.
One thing you can try is to raise the eye from the back side with a rounded tool large enough so that is doesn't leave small marks in the leather or maybe a modeling spoon.
Keep thinking and trying different methods on scrap until you get what you want or a result that you are happy with.
I have your picture so I can experiment on it a bit, not that I know what I'm doing but it's hopefully better than no help at all.
Kevin
At 1 I think you need to bevel the eyeball to get rid of that sharp edge and at 2 I think that needs to be cut and beveled in the same manner.
It's not that far out when looking at it when made smaller and a little tweaking is all it needs but do it on scrap first, that's what I learned on the dog carving.