If you can put the mixture into your broken tooth without discomfort, you should be fine until your dental appointment. To reduce possible pain while eating, you may want to stick with soft foods and liquids, avoiding anything too hot or cold. You could also try chewing solely on the intact side of your mouth. If you find it impossible to eat, or are generally extremely uncomfortable, your dentist may suggest you squeeze yourself in for an emergency appointment. Normally, chewing gum does not cause teeth to break.
Some gums do tend to stick to artificial dental work, such as dentures or a bridge.
If this is an issue, try a gum especially designed not to stick. Keep in mind that teeth usually break for a reason. You might have some decay under a filling or around the broken tooth. Sometimes, if a tooth is severely damaged, and has a large filling, the tooth will fracture because so little of the tooth is actually left. Alice is happy to provide you with this information.