The most important thing was to get your grades up, and you've started to do that. While they're higher, depending on the group, it still may not meet their minimum for a new member. Some may require 2.75 or 3.0.
For your own sake, I would encourage you to try to get them up even more, regardless of whether or not you join a sorority. A low GPA will hurt you a lot in looking for a job and/or getting admitted into grad school.
Since you've been in school for awhile now, I don't really think anyone will care what you did in HS (well unless you did something really bad like kill someone's cat or something). So there's no real need to bank on that. No one in college is really going to care
That's one of the great things about college, you sorta get to start a new slate.
I have to ask WHY you want to be greek? Why is it important to you? I think that's an important question for you yourself to know the answer to before you make any decisions. Doing it for the social life isn't really the best reason. YOu don't have to answer, it's more of a rhetorical thing that you should think about.
Also, how are you going to be able to devote the time to being greek if you're working 25-35 hours a week, taking classes, tutoring, etc? That's gonna be a question that a sorority would ask itself about you. Is this girl going to be able to do much for us?
And at some schools, if a group has cut you before, it's very likely that they will cut you again. Especially if you had been fake the first time around. If anything, be pretty open and up front about your mistakes.