No your mom doesn't need to. You have to file your own return if you have income no matter how young you are, even if someone claims you as a dependent. But if you live with someone else for the whole year and you made less than 4,300 total income then they can probably claim you even if they are not related to you. So if you live with the Grandma maybe Grandma can claim you.
Here are some rules if someone can claim you,
Who can you claim
https://ttlc.intuit.com/community/credits-and-deductions/help/who-can-i-claim-as-my-dependent/01/267...
See IRS Pub 501 starting on page 10 bottom Dependents and Worksheet 2 page 15 for determining support,
https://www.irs.gov/pub/irs-pdf/p501.pdf
