Another UM grad here--and agree with what Sciencewoman said (and so glad her chapter is back!!
). My pledge class was probably half sophomores. Granted, that was a while ago, but my understanding is that MOST sororities are still open to sophomores.
Please, please, please go in with an open mind. Yes, you may know girls in certain houses, but you will be joining an organization of over 100 women and will be spending time with all of them. All the sororities at Michigan are fantastic in their own way. Don't worry about what fraternities they pre-party with or the "tiers" or whatever. Your sorority experience is what you make of it.
As for explaining why you didn't rush Freshman year, I think it's pretty common, but I think you can explain that you were getting used to school and your small program and you wanted to get used to college life.
You sound really enthusiastic and like you want to join for the right reasons. Just be yourself and it should work out.
Good luck! Joining a sorority at UM was the best decision of my life. I hope you are lucky enough to experience that as well. (And yes, let us know how it turns out!).