I was under the impression there is no real consensus on the first sorority, there were "womens societies" in 1851 that fit the bill in some ways and did adopt greek lettering much later on. The first sorority to actually be called a sorority was Gamma Phi Beta in 1874. There were at least 2 other "womens fraternities" that used greek lettering in the early 70s but didnt adopt the word sorority till after.
Googling aside, i dunno if i would wear them to a support group meeting, im from the UK so i dont really fully understand the significance but there seems to be something unwholesome about wearing letters of brotherhood to group of trans folk?