Urgent care doctor not seen for 2 hours. Are they ignoring me?

This must be from. Your hand held or i-pad1! you should tap on the window and ask the receptionist if this common, and how do they triage (rank order patients by seriousness of complaint) rather than at time of arrival. Google others and call asking what their wait times are. Two hours seems excessive without an explanation.
Busy. Urgent cares are generally 1st come 1st serve offices. They usually do not prioritize because seriouslly ill patients should be going going to er.Thus they are probably just busy.