It would be your mom's insurance policy that would be adding you to her policy. The alternative is to get another policy for you and your mom on your new car or with her car and your car together.
You can easily obtain insurance for your car. Some insurance companies may require that you be the policyholder if the vehicle is in your name only. Others will allow your mother to insure it for you. Some will even allow your mother to insure her vehicle on the same policy.
If you determine that you will buy your own insurance policy, your mother will need to confirm the policy coverages along with you due to your age.
You can obtain a direct insurance quote here to determine which insurance companies will insure you.