A lot of people do knit tightly when they start. It doesn't mean anything's wrong. Bigger needles might help, but I wouldn't go buy more just for one project; after all, it's a dishcloth, and the knitting police aren't allowed to climb in the sink and measure it.
If you add stitches in pairs, you can make that pattern as wide as you want. (If that's wrong, somebody fix it. I'm fogged out from this cold tonight!) Once you knit for a while, you may find you don't knit as tightly, or you may find that you do. As long as you're happy with it, it's not a problem. When you get to projects that have to be on gauge, you'll know to use a slightly larger needle, that's all. By then you'll know what kind of needles you like best and what set of interchangeables or fixed circs to put on your gift list