In the US many people would not understand that "my arm hairs stand up" really means "I have goosebumps". The closest expression I can think of is "It makes the hairs on the back of my neck stand up", which has the same meaning as "it gives me goosebumps". We can use these expressions for both things that scare us and things that amaze us.

You would probably sound a bit strange if you said 'my hairs stand up'. There is another common way to say it and that would be: 'my hairs are standing on end'. It would sound a TINY bit strange, but I have definitely heard people say it before, and it is not weird!

My arm hairs are standing up. Understand? Sure. Everywhere else, no problem. ...are standing on end

Hola!! Claro la podrías ocupar, pero en un español empleado en México, se ocupa más la expresión "se me puso la piel Chinita".