Newbie question - backstroke "stroke"

At first I thought I liked the backstroke, but now I'm all confused about the stroke. I started doing the stroke "not thinking about it", but now that I'm _trying_ do it right, I can't do it anymore. =) The recovery phase is fine -- obviously, it's relatively easy. My hand is in front of me and I'm not doing anything too crazy with it. It's the push/pull. I find it awkward to do much of anything behind my back, perhaps because of low flexibility. During recovery, my arm stays in the vertical plane, close to my head. But once it enters the water, it tends to veer out of that plane and to the side because I can't put my arm behind my back with my palms facing my feet very easily. Since my stroke goes out to the side a bit, it steers me off course and destabilizes me. While writing this, I'm practicing my stroke in the air, and I just noticed that rolling into the stroke makes a HUGE difference for me. My instructor didn't tell me to do that... I'm beginning to wonder how good she is... she's a good swimmer... effortless in the water... but she doesn't verbalize very much. Ahh, rolling, maybe I answered my own question. My shoulders REALLY hurt when I don't roll, but when I do, it feels great. That definitely helps. Okay, I have one more: I don't wear goggles when I swim and I find that even when I minimize the splash, I still get water in my eyes during backstroke. Should I just swim with my eyes closed, will I get used to it, or what?