I am 16 years old. I swore that I would not eat a certain dish. Is my oath permissible?

Your oath is binding because you are an adult. If the intention of the oath was to refrain from eating in general, then breaking the oath is obligatory. If the intention was to refrain from a specific type of food, then breaking the oath is preferable and permissible, based on the Prophet, peace and blessings be upon him, who said: "Whoever takes an oath and then sees something better than it, let him expiate for his oath and do that which is better."