I am a software engineering student who is thinking to build a Dashboard for ER waiting times. Potentially it could tell your whether a longer trip could still save you time. There's currently no way of knowing what the waiting times are for the ER in the various public hospitals. There is an inefficient distribution of ER resources with unnecessarily long waiting times for ER patients. I am wondering if there is any liberated waiting room data (e.g. tracks bed vacancies across the country's hospitals)? Thanks!
There is no one source that I know of for realtime wait times though some larger networks do have apps or mobile sites that you might look into scraping though of course that has many disadvantages.
In terms of historical data, ProPublica has some great data and analysis at https://projects.propublica.org/emergency/
I believe the sole source of the ProPublica ER wait time site is CMS Hospital Compare data which can be found at https://data.medicare.gov/Hospital-Compare/Timely-and-Effective-Care-Hospital/yv7e-xc69