Does Turbo Tax calculate and include the social security and Medicare taxes on my independent contractor income?

Yes.  TurboTax calculates these taxes automatically on independent contractor income and includes them on your tax return.  They are called self-employment taxes and you will find them on line 57 of your Form 1040.  Also, a Schedule SE will be attached to your return showing the calculation of these taxes.

I went to a SSA office locally and it do not appear as reported from my Turbo Tax since it was filed on 2017,2018,2019. They said I have to go to IRS to resolve this issue. I am still in need !