Mr. Spock's half-brother Sybok is emotional and basically crazy. He doesn't follow the Vulcan's way of logic so does that mean he's a Romulan?
No, Sybok was Vulcan.
Sybok was the son of Sarek and an unnamed Vulcan princess. He is biologically %100 Vulcan.
Sybok did not want to follow the teachings of Surak. This is indeed what the caused the Romulans to split from the Vulcans in the first place, but Vulcans and Romulans are physically different as well, as detailed in the linked answer.
So while Sybok may emotionally have been more Romulan than Vulcan, there is a biological difference between the two species, and Sybok is a Vulcan.
Sybok was a vulcan
He was technically a Vulcan, no denial but you could say he acted like a Romulan, or rather he acted like Those That March Under The Raptors's Wings (ancestors of the Romulans that defied Surak) but Romulans stopped being Vulcans a long time ago when they started evolving and breeding so that they got their V shaped foreheads.