I rushed at an SEC school as a sophomore and got my first choice!
Granted, UK isn't Ole Miss or anything like that, but I can name 3, maybe 4, sororities off the top of my head that you pretty much will not get into if you are a sophomore, so yeah, I'd say it is competitive to an extent. Get your recs, even if the rush application says you don't need them. And I agree with whoever said go out and meet sorority members...knowing girls in about half the houses did work to my advantage.