I am a full time college student and also a recipient of federal work study. Taxes aren't taken out of my paycheck, will I still need to file taxes next year?

Depending on the amount you earn, you may need to file a tax return.  If you are a dependent and the total is less than the personal exemption ($12,400 for 2020) you would not have to file a tax return.  

Except in rare cases, work study is treated as any other job but also counts as part of your financial aid. You should check with the school- you want to make sure they have the correct information for withholding.

If you are a full time college student under age 24, if you do not pay for more than half of your own support (including tuition and living expenses)- your mom should still be able to claim you as a dependent.

How was the income reported to you; W-2, 1098-T box 5, 1099?

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC, so you mother's ability to claim you as a dependent is usually  not affected by this income.