im sure somebody should yell at me for this but i dont even tighten the pedal nut down with a tool sometimes and just tightest i can with my fingers because if i'm not mistaken, the direction of rotation is designed to be opposite of loosen so = tighten, meaning it'll get tighter and tighter as you ride.
do make sure the threads on both the pedal and the cranks are well greased (Park Polylub should be enough)
and when you can, ride it to your lbs or a car shop, they'd be happy to freely lend you a 15mm open wrench or even a pedal wrench just to be nice.