I received a ssa-1099 form from where I received money from back pay after my mother's death do I need to file that with my taxes and how?

Yes, you would file it on your taxes since you received the income and the SSA-1099.

According to the IRS:

When a taxpayer dies, a new taxpaying entity – the taxpayer's estate – is born to make sure no taxable income falls through the cracks. Income is taxed either on the taxpayer's final return, on the return of the beneficiary who acquires the right to receive the income, or if the estate receives $600 or more of income, on the estate's income tax return.

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