I am breastfeeding my son and i have fallen asleep with his head resting on my arms. i wake up with arm hurting. am i doing long term damage to arms?

Unlikely: unless you have some sort of pre-existing nerve damage, it would be highly unlikely for a baby's head just resting against your arms to cause any permanent damage. Think of it as your leg falling asleep. Some sort of compression lead your nerve to tell you that something is wrong, so that means you should not leave your baby's head there for too long, but your body is giving you a sign.