No.
The estimated tax payments are only for federal income tax.
Employees are charged Social Security and Medicare tax only on their Wages, as reported on your W-2.
If you are self-employed, then the Social Security and Medicare taxes are called "self-employment taxes", and are reported on Schedule SE.
The SE taxes are added to the federal income taxes on form 1040, and all estimated taxes are applied against the sum of the two.
Questions?