Did alexis bledel really break her arm or was it simply part of the show?

You're likely thinking about a scene from the show "Gilmore Girls" where Rory Gilmore, played by Alexis Bledel, gets her arm broken.

It was part of the show, not a real injury.

In the episode "That's What You Get, Part 2," Rory's arm is broken by a runaway shopping cart.

While Bledel was skilled at acting, she didn't actually break her arm for the show. The injury was achieved using special effects and makeup techniques to create the illusion of a break.