If we can't do urgent care, is it ok to go to emergency medicine doctor?

If emergency: Only if it is an emergency. If it is just a medication refill, minor complaint, question about a chronic problem, or something that can seriously wait til the next business morning, do not go to the er. That is a waste and uses resources and personnel that are needed for true emergencies. But if a true emergency, then go to urgent care. If you can't, then er is fine.

Of course: Part of emergency medicine is being prepared to take care of every patient who doesn't have access to another physician. Although most emergency physicians would prefer that non-emergent issues be dealt with by a patient's primary care physician, at the end of the day it comes with the territory and the most important consideration is that patients have access to doctors.