I get severe 10-30 second headaches after I laugh or sometime move my head too quickly. Could this be a back/chiropractic issue? If not what is it?

Vague. Impossible to say without a thorough history and exam. Actually, could be an inner ear or sinus issue. Or it could be a neck issue. Should really be seen before it gets worse.
Depends. It could be related to your neck more than your back, but there could be a back component too. If it's a musculoskeletal strain after laughing so hard causing a headache, this could be possible. You should get a 2nd opinion from a neuromusculoskeletal doctor (NMM) who's a osteopathic physician to get a full evaluation, and treatment done. Will be very helpful and informative.