I played quake constantly in the 90's. Never ONCE got sick.
Just for the hell of it, I went on EBAY and found the original quake. It was identical to the one I had in 1996. After playing it up to the third level, I started to vomit . I don't know what I am going to do, because it is making me hellasick. Especially in the areas where I have to swim and rise to keep from drowning. I actually feel like I am gulping water when it makes that "blub blub" sound. I hate to medicate to be able to play. There must be something a person can do.
Could be the result of simulator sickness. These things change as we get older man.
Part of it could have to do with the difference between playing on a CRT in 1996 and playing presumably on an LCD now. LCD's have some measure of ghosting, where CRT's really didn't have any. Also try widening your FOV. A narrow FOV will make things around the peripheral of the screen exit the screen faster and give you the illusion of faster movement.
Good luck. I wouldn't recommend bothering with any medications though. If adjusting your FOV doesn't help, it might just be a sign that it's time to move on from Quake.