Well the 13s aren't going to help much. Try a size 5 to 8 needle and see if that's better. You do want a loose knit for a shawl, not tight like you would for socks or even a sweater.
eta - Oh, if it's a worsted weight, then maybe go for an 11, a 13 can work for a lacier look though. Also, wash and lay out what you've got knitted, that will even out the sts.