The diamond-shaped pin is a member pin for Psi Iota Xi, a high school/community sorority that was founded in Indiana in 1897. I determined this by searching for other examples of that same crest. (I knew it wasn't an Alpha Chi Omega pin because that is not the AXO crest.)
I searched for "crest lyre pin" and located the above example - same crest, different mounting. In this picture, I could now see that Psi Iota Xi is in the scroll at the bottom. Searching Psi Iota Xi quickly turned up the sorority online, still in existence.
Reference:
https://www.psiiotaxi.org/
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