Hi David!
I’ve had that feeling before, too. It turned out that I was very dehydrated from sweating so much.
Do you take in a good amount of water before, during, and after your workout? I usually take a 20 oz water bottle with me for any workout. I’ll drink 1 bottle in the 1/2 hour before my workout, and 1 bottle for each 1/2 hour of sweating I’m doing, and then another bottle on the drive home. This little “one bottle per half hour” rule of thumb seems to work pretty well to ward off and lightheadedness or otherwise sick feelings.
Also, what are your typical eating patterns before and after a spinning session? The sick feeling could be linked to not having enough energy (food) to push your body has hard as you’d like. You should typically give your body a light, energy-packed small meal about an hour before your workout. Half protein / half carbs will give you body a great boost through your workout.
Does this help?