FYI: The specialist skills are better than the generic treatment or diagnosis skills. So Pysch 1 + 2 is better than Psych 1 + Diagnosis or Psych 1 + Treatment.
Also, as for your overflowing issues: Open the patients list and sort by status, putting the “reception” symbol at the top of your list. Watch it for a bit and as soon as a new person joins that list click on them and watch them get out of their car and walk into your hospital etc. Follow them through and hopefully you should see why there’s such a slow-down and what all of the stuff they walk into on the way is.
It’s probably in your reception / GP area. e.g. Maybe the corridors need to be 3 or 4 wide instead of 1 or 2? Or maybe you need more “stuff” for them whilst their waiting in the queue, and fewer chairs?