Even for those obvious things 90% of the insurance companies require that you follow their steps, which is go to the primary care first, get a referral to and then see a specialist. The only ones that I can go in to see without referrals is my eye doc, my primary care, and urgent care. Anything else? You better have a referral or you will be fighting an uphill battle to even have them consider covering it.
P.S. In my insurance ophthalmologist is considered as a specialist. I assume you are talking about optometrist when you say "eye doctor"...?