PLEASE don't resign. Your membership is for a lifetime. Based on your well-written post, you'd be an asset to your fraternity(sorority) in the future, and even now. Your experiences will serve you well, trust me on this.
You are being tested. Are you going to let that small group of women take away your lifetime and all the positives you'll get as a Panhellenic woman?
There are 8 stay reasons and only 6 leave ones. I think that should inform your decision and I also agree with AZTheta. Don't throw away lifetime membership. Also, just a suggestion....nowhere in your narrative is anything about talking with your advisers. Perhaps that's the missing piece.
Spinowl, I hope you'll stay. Many of us have had to deal with catty girls not only in our chapters but also in other clubs. Well heck, learning to deal with that is good experience for future experiences overall. It's not only limited to new chapters and it's sure not limited to the high school and college years.
Hang in there! Find yourself some likeminded sisters and get to know them!