Optomitrist is one level of eye doctor, there are also ophthalmologists, which are a step up. Keep trying.
I found myself with a bothersome eye issue a week or so ago (I'm 75). I had a very distinct spot of non vision at the center of my field of view in my left eye. It was Thursday afternoon. I called my eye doctor and he had me in his chair within a couple hours (came in special to take a look). He referred me to a vascular eye specialist because the issue has to do with a microscopic blood clot in the eye. He told me to let him know if I couldn't get a quick appointment; don't want to sit on this for long. I was offered an appointment on Monday (first business day after my call), but was tied up myself so went into his clinic on Wednesday. He did his tests, confirmed the diagnosis, and gave me two shots in my eye(!), which were painless, and set up an appointment in a month to confirm that they resolved the issue. None of this will cost me anything out of pocket.
Tell me again why we need socialized medicine. I forget.