Headedness and dizziness, should he continue benicar (olmesartan)?

Experiment. Did symptoms start only after starting the Benicar (olmesartan) or did you use to have them before also? If yes then you can hold Benicar (olmesartan) with permission of your pcp. If symptoms disappear for weeks then Benicar (olmesartan) is culprit. If symptoms persist then there is some other cause like migraine.
Seveeral issues. The Benicar (olmesartan) may be causing to low a blood pressure. Point two is this. If you have had an appreciably elevated BP for some time, even lowering BP to normal may decrease cerebral flow. Talk to your prescribing physician. Also, losartan is a generic arb, works like benicar, (olmesartan) and is cheaper.