My ear is throbbing with pain on and off but my mom doesn't believe me. Is it a ear infection?

Possibly. Pain from ear infection is typically constant but might throb intermittently. I take it that you are younger by the way you posted the question; kids and adolescents are prone to ear infections but also to dental problems and jaw issues (tmj problems). If the pain continues, show this answer to your mom, telling her to take you to the doctor!
Probably your jaw. Probably referred pain, not the ear but the jaw joint and the muscles that move the jaw. Don't chew gum, stay away from crunchy foods.