You don't need to be in a dire emergency to visit the emergency room. If there is a non-severe medical issue and your doctor can't see you, then you are advised to go to the emergency room. Nowadays, you can go to private medical facilities, like Patient First, that provide emergency room-ish services where the severity of the medical issue is not severe, e.g. flu, minor cuts, sore throat, headache, pain, etc.
I think there are plenty of options before heading to the ER. A good physician group should have someone on call and they might be able to call in prescriptions to a 24h pharmacy.
I think the idea that there's only one option kinda shows why nothing ever gets fixed, eh?
I should probably delete the above post before someone takes it the wrong way and laments the fall of society... I'm not being political, though. I'm just explaining what I've observed.