Do I need to file amended tax return in order to receive my unemployment tax money back after filing my 2020 taxs with the new law

You will have to amend the 2020 tax return that was filed to receive the unemployment compensation exclusion.  But do not file the amended return until guidance from the IRS has been received.

After the legislation has passed Congress and after the President has signed the legislation and after the IRS has written the rules, regulations and procedures.  And after the IRS has changed any forms or schedules to accept the tax code changes.  And after the IRS has approved the changes in the TurboTax program that apply to the tax code changes, then it will be available for the users of the tax preparation software.

This can take anywhere from several weeks to several months before it becomes available.

See this TurboTax support FAQ for information on the American Rescue Plan - https://ttlc.intuit.com/community/tax-topics/help/how-will-the-stimulus-package-impact-

I would also like to know when we can file an amended return for unemployment taxes paid