I am playing the GOG version of Doom 2 (Ultimate doom just hangs on title screen, so I've given up) and it seems like there is a lot of horizontal tearing as I turn the camera back and forth. Is there some way to enable some sort of v-sync like option? I play fullscreen on a CRT.

Some source ports have the option available, GZDoom is one that comes to mind - https://zdoom.org/downloads

Though you didn't mention if you prefer not to go the source port route and want to stick with the DOSBox experience instead.

Use a source port. If you want a vanilla experience then use ChocolateDoom, if you want additional features and the option for prettier graphics then use GZDoom, and if you want to go multiplayer then use Zandronum.