The words you choose within an app are an essential part of its user experience
The “it looks like you’ve blah blah” example is terrible, imo. The last thing I’d want to deal with after a hard fall is this chatter.The correct way to do it is:  (Attention sound)
  Did you just fall?
  ((SOS) swipe for help)
  [I’m okay]

The original message doesn’t even mention it’s a swipe. I can imagine a stressed person trying to tap that message or icon without realizing it doesn’t work. Targeting at eldery you must be crystal clear, not subtle-UX-clear.