Here in the USA, AT&T (actually, it's the hold-over from what we call the old "Ma-Bell" before the split up into AT&T and others) handles the Phone # <-> Address databases in a few regional centers around the country. That information is sent to the local/area 911 Dispatch centers so that the dispatchers can see where you're calling from (things are a bit more complicated with E911, mobile, and texting 911 but, still, the basics are the same for what you're talking about).
With the situation you're in, it's very much like the private hospital / flight EMS services, such that you're going to have to build a database that matches up phone #'s to physical locations (addresses if you have them .... GPS coordinates or maybe 'directions' such as "200 meters South of that hill known as Bald Ridge" or something like that) that responders are going to be able to work with to find the person ... or at least get close (they may be in the field and not at home).
So, a call comes in ... the person may be able to talk or maybe not. The dispatcher at the hospital sees that it is from cellphone # 12345. The software with the dispatcher does a lookup on that number in the database and sees that that # corresponds to a GPS coordinate of lat, lon. or of a 'directions' text. No other way around it. You have to have a subscriber service if you have no other automatic means to get it. That's what Ma-Bell does for 911 but just on a MUCH larger and automatic scale. The problem comes in keeping those records updated. HUGE HUGE problem. A nightmare, really, for any non-trivial-scaled project.
If the phone has GPS and (here's the kicker!) that information gets passed along to the dispatchers / receiving end, then things are much easier and accurate to where that person is actually located instead of where the phone # is subscribed to be (ie a home).
I'm not sure where an app is going to help you. Unless you're talking about the ambulance crew having smartphones and getting information from the dispatch center?