Do you think my mom is right in this situation?

Your teacher does need to know--that's probably lost income. You might talk to your teacher about other instruments your teacher might offer instruction in. Set yourself a goal for that last month and try to reach it.. Your teacher may have a suggestion or two for you so you won't lose what you've learned so far. Your mom is right that you need to consider others who may be affected by your plans, you're right about probably needing a break, and maybe you can enjoy the time.