Yes, you can buy, title, and register a car even if you’re under the age of 18. Since people under 18 can’t enter into an insurance contract by themselves, getting a policy can be a little tricky. There are some carriers that will write a policy for your mom, even though she doesn’t have a license. And since you live in the same household as her and have an active license, you can be listed on the policy as the driver.
Each insurance company has its own guidelines and acceptable risks. In this situation, it’s best to be direct with your insurance agent so they can make sure that everyone is properly protected.