The answer to your question is
GC §411.203. RIGHTS OF EMPLOYERS. This subchapter does not prevent or otherwise limit the right of a public or private employer to prohibit persons who are licensed under this subchapter from carrying a concealed handgun on the premises of the business.
It is not a criminal offense to carry with a CHL on public property that is not an off-limits place such as a school.
However, do not expect every LEO to know that. If a LEO thinks you need to be arrested, you're going for a ride.
I have no clear thoughts on armed EMTs, but I know that there would be a huge furor if arming them were proposed. Many medical personnel are anti-RKBA, and most big-city governments and police chiefs are also.
- Jim