The part of the eye that is similar to a contact lens is the crystalline lens.

I have a prosthetic eye. It's like a contact lens, and it goes in similar to a contact lens

A contact lens rests on the tear layer of the eye. If the tear layer has evaporated and the contact lens is stuck to the eye, SEEK IMMEDIATE ATTENTION. Never try removing a contact lens which is stuck to the eye. An Optometrist or Ophthalmologist is your best bet of removing the contact lens safely without damaging the cornea of your eye.

It really depends on where you live. If there is an America's Best in your area, they have inexpensive contact lens eye exams.

Someone can purchase a non prescriptive cat eye contact lens from any local store near them.You can also purchase a non prescriptive cat eye contact lens online for cheap.