You can set a Lock Screen Message by searching for "Lock Screen Message" in the Android Settings.
You can also create an "ICE (In Case of Emergency)" contact.
I wonder if dialing 911 from their phone would give emergency services some helpful info. Do they automatically get caller ID (perhaps enhanced)?
A lot of areas have the ability to query a cell phone for its location, but it depends on how much that city/county/state(?) spends on 911. It's usually based on carrier location (so it's not really that helpful anyway), and calling from their phone probably won't help much since you're both in the same location. Caller ID might help if they have a recurring problem (like if they have epilepsy or something that the medics that show up would need to know), but for a concussion it's pretty unlikely they had called 911 before so it probably wouldn't have done much. I remember reading something about iOS sending medical cards somehow when you call 911, but I don't think that's a feature yet (and it relies on iOS, so if they didn't have an iphone it wouldn't help anyway).
Source: I help test emergency boxes (the things with the blue lights in parking lots), landline phones, and cell phones at my job every year. I have to confirm different info based on what I'm calling from. On cell phones, it's just the number the call is being made from. By the way, if you're wondering, 911 does not appreciate hundreds of test calls being made unannounced over the course of a day. We do it anyway :^) (we're required to)