Unfortunately,
YES, the Gun Control Act of 1968 prohibits the shipping of any and all firearms made after 1898 between unlicensed individuals.
You need an FFL to ship to another FFL holder or to an individual.
You, as an unlicensed individual can ship a gun to a FFL holder for repair, customization, and refinishing, etc.
Improper shipments of firearms are confiscated by the Postal Service.
A cousin in the US Postal service advises that they do 100% package x-rays for security.
The various shipping companies notify authorities of gun shipments.
John