Yes, you might try a larger hook to see if that helps with the yarn splitting issues. As far as crochet patterns go, I think most of them can be worked either left-handed or right-handed without too much trouble. In crochet you don't really have left-leaning and right-leaning decreases like you do in knitting, so that shouldn't be a problem.
However, you might want to search on YouTube to see if you can find some left-handed crochet demos (that is, if you need help holding the hook and yarn). The stitches themselves should be made the same regardless of which hand you use to hold the hook.
Oh, and there are lots of square patterns (many are potholders), which can be made from side to side or starting in the middle and working your way out (ala, granny squares).