When removing bolt-on wheels, it’s best to only slightly loosen each nut at a time. You don’t want to completely remove each side in one go, because then you get your current situation, where the other side refuses to come off. You end up spinning the entire wheel along with the nut, so it won’t unscrew. Loosen the left side an quarter turn, then the right side a quarter turn, then the left side again...and so forth. I would do up the nuts tight again and start over. Perhaps begin by breaking loose the other nut so you’re sure it’s not corroded in place or something.
You might want to consider using a proper 15mm wrench. I presume you’re using an adjustable wrench, which isn’t very precise and can strip nuts and bolts (as you’ve discovered) if even slightly too loose at high torques. Basic wrenches are available at hardware and automotive stores for like 10 dollars, so it’s a worthwhile investment. For a couple extra dollars you can upgrade to a ratcheting wrench which will make the job slightly faster.