If you meet the requirements to file as head of household you can file as head of household whether or not your mother files a tax return. Whether she files a tax return is not one of the considerations for you to file as head of household.
If she had federal tax withheld from her Social Security benefits, she should file a tax return to get a refund of the tax that was withheld, even if she is otherwise not required to file. Federal tax withheld would be in box 6 of her Form SSA-1099.
