No. People who are older than that have a smallpox vaccination scar on the shoulde from the vaccines in 1958-1977.

The arm thing s is just an urban myth and plays on confirmation bias. Almost everyone have a freckle there for no good reason.

However… Mexicans actually have a tuberculosis vaccination mark on the arm, but most other countries didn’t need to vaccinate against that.

That’s how these myths spread, part truth+loads of bullshit.