Another bit to note is that you can sometimes experience pinching in your mouth along the fleshy inner part of your cheek close to your teeth because the braces sometimes poke or cling. The wire that runs through the brace can poke the back of your mouth if it's not clipped cleanly at the dentist so before you leave your dentist after every check up be sure to swish your cheeks and tongue around and make sure you don't feel any pinching or pricking anywhere.
To answer your question Ingredient gum is a big no no when you have braces. Unless it's sugarless (I know what fun is that right? lol)... however that isn't to say to still use caution. Sticky, chewy, and or hard food can damage or break the hard ware in your mouth and cause you to take an emergency trip to the dentist (trust me I learned the hard way quite a few times cause I was stubborn at first lol). If you break the braces you'll only be making yourself uncomfortable, angering the doctor because you're wasting expensive stuff, and prolonging the process. I broke my braces by snapping the metal wire that runs through them a few times. I couldn't give up my steak lmao. Eventually you'll grow new methods of chewing that could possible help you to still sneak some naughty foods in but as a word of advice I just don't recommend it lol.