Absolutely, 100% consider migraines. Headaches are far from their only symptom, and headache-free migraines are a thing. Nausea is a common symptom. It's worth a try, and the medication is generally safe with few side effects. Consider talking to your neurologist or finding another that specializes in headaches.

Start with triptans (which your insurance may insist you do anyway), which are very cheap, and then try a CGRP blocker like Nurtec, which is patented and expensive. I get migraines, but nausea, depression and tiredness are far bigger effects for me than the actual headache (which is normally controllable with OTC drugs). CGRP blockers have been life-changing. It took them years to diagnose me with migraines, in fact I had to suggest it myself.