Should my arms hurt when I am blocking?

Well of course to start with we would need to consider your experience and what you are blocking, but in short, no it shouldn’t.

Providing that you have the correct use of energy.

Even then though energy is not the only element, timing will also play a huge part in this, in the exact way we may use energy to jam a Pak Sau.
If the energy used is too late or too early or even too little, then it will simply not be affective.

I often mention a comment I heard from a football coach, which referred to the use of energy when he said, ‘If someone kicks a football across a field and it hits your head, then it will hurt, but, if someone kicks a football across a field and you hit it with your head, then it does not hurt’.

This is the same as our arms when we are blocking.

To stand in a ready position and let the attack hit you, it will hurt, but if you use the blocking position to attack the attack, then it will not.

Energy, timing and obviously the correct structure to start with, and your blocking should not hurt your arms.

Although perhaps avoid trying to use Bong Sau against an oncoming train eh?
Energy, timing and structure do have their limits. 🙂