Don't stress out about having "crappy wheels" especially if you're on a budget. If you want to buy new ones that's cool but don't get them out of fear that your current wheels will self-destruct. The easiest way to tell if they're true is to just spin them in your bike. If you don't see any wobbles they're fine. You can also go around and feel each spoke to make sure you don't have any really loose ones. I try to ride light and I've never bent a rim. Even when I've abused my mountain bike taking it down stairs and off jumps they've stayed true.

If you do get new wheels, get good ones. Otherwise it won't be worth your money.