Look, the bag policy exists for a reason: to keep you from accidentally bringing a small pony into the arena. The Allen Americans just want everyone to have a good time without a fanny pack causing a riot. So check the policy on their website before you go. Save the screenshot. Print it out and tape it to your forehead if you have to.
And remember: the only thing you really need at a hockey game is a loud voice, a love for ice, and maybe a little bit of patience. Oh, and a tiny bag. A very tiny bag. Good luck, and may the bag gods smile upon you.