This app was mentioned in 8 comments, with an average of 1.00 upvote
https://play.google.com/store/apps/details?id=app.medicalid
Has a "call these phone numbers" feature.
Medical ID (Life saving app)
link me: Medical ID (ICE): Emergency
https://play.google.com/store/apps/details?id=app.medicalid&hl=en
Medical ID provides an alert mode that allows to send an SMS along with GPS location to defined contacts when clicking on a button.
I have used this app on my earlier phones: Medical ID: ICE