What airline are you flying on? Also, what pound ball do you throw? If you throw 15, you should be OK with just the 3 balls and your shoes, dont try to pack anything else in there.
I also used a cardboard box, and I regret it. It seems like it would be a great idea, but in the long run it sucked bad. It was a real pain lugging that damn thing around. I took a box that was a little bit bigger and put a small 2 ball tote, a bad of clothes, and a small sleeping bag in it. Like I said, I thought it would be really convenient but this was my first time flying so I didnt really know. It sucked, but it worked. Good luck.