Should I see a specialist for non venomous snake bite, or can my regular doctor take care of it?

PCP good. You should get it checked by your doctor who can evaluate for infection, inflammation, etc. - if he/she feels it necessary for you to see a specialist they can direct you to the proper specialist.
Your doc. For non-venomous bites, your primary physician should be able to advise and treat if any secondary side effects occur.