Welcome!
There are lots of women here who have gone through the alum initiation process... I'm sure they can give you some insight.
Alum initiation policies range from "we don't do it at all" (AEPhi is in this category
) to "you have to have a relative who's a member" to "anyone can try for alum initiation".
From what I've read here, your best bet is to choose one and only one group to pursue, contact either their national office or local alum chapter, maybe get involved with a collegiate chapter if there's one nearby, and go from there. The process can take months or years, so be patient!
Good luck!