It certainly won't hurt, partial water changes are nothing but helpful (provided your tap water has a chemistry reasonably similar to your tank's water).
Go down to your LFS and pick up test kits for ammonia, nitrite, and nitrate, you're going to need them down the road anyway.
Pop-eye can have several causes, sometimes it's a gas build-up in the blood stream if the temperature rises too high (unlikely in an unheated bowl), it can also be a bacterial infection. Can you describe the eye in greater detail? Can you see little "bubbles" in the eye? If it is bacterial, your best bet would be some sort of anti-biotic. There are all sorts of brands out there, just find one that says it treats "pop-eye."
Pop-eye is almost always caused by water conditions, whether it's a temperature that's too high, or high level of nitrgen toxins. It can be treated, but it's more important to find the cause. Testing your water will be a good start at finding the cause.
HTH,
Josh
