I only know the short story - the medal is based on apparitions by Our Lady to St Catherine Laboure in Paris (in 1830 - hence the date ‘1830’ appearing on the medal underneath Mary’s feet, if you look closely). And it gained the nickname ‘Miraculous Medal’ because of the many stories of miracles that occurred to people who began wearing it.
I wear one and regularly say the prayer written on it - ‘O Mary conceived without sin, pray for us who have recourse to thee’. Interesting that it says ‘conceived without sin’, since the Immaculate Conception of Our Lady (the dogma that she was indeed ‘conceived without sin’) wasn’t formally proclaimed until some years afterwards.