This appears to be a generic pin ordered by hospitals to give to candy stripers, because the trademark for the little coat of arms and "NISI DOMINUS FRUSTRA" was registered to a hospital supply company. I think your date of 1960 is about right, from the hyphenated teen-ager, and also it's a clear echo of nursing pins, which are given to nurses at graduation and unique to each nursing school, these are not worn so much these days (my sister doesn't wear hers to work) but in the era of the white hats they were a more prominent part of a nurses' uniform. (My grandma told me a story this Easter about how she lost her pin off her uniform in the hospital laundry in the 40s and she was so upset and had to call her school and buy a new one!) Candy striping is often done by young people interested in a career in nursing, so that's probably why they gave them out, because the girls would enjoy them. Neat find though!