You know what, I read your post wrong and thought you said you DID feel sick. My bad!
Before I can answer your, what do you do for a workout in the morning? Short and not too intense cardio is fine. Longer, or intense cardio would not be a good idea, and strength training would not be a good idea.
Here's a little research on the subject for you:
The Claim: You Burn More Fat by Exercising on an Empty Stomach
By ANAHAD O'CONNOR
Published: April 4, 2006
THE FACTS For most people who exercise in the morning, there is no getting around the question: Eat and run? Or run and eat later?
Fitness experts will say that eating first provides fuel for a proper workout. But according to one common belief, exercising on an empty stomach forces the body to tap into its reserves, burning off calories stored as fat and providing a more efficient workout. So who is right?
According to researchers, there is no simple answer. One study that examined the claim directly in 1995 found that a group of people did burn more calories from fat on days when they exercised on an empty stomach than on days when they had a small breakfast first. But the researchers found that the difference was negligible, and other studies have shown that fewer calories are burned in the long run because the workouts are shorter.
A study published in 1999 in the journal Medicine and Science in Sports and Exercise had a group of people ride an exercise bike on two mornings: on one day after a small breakfast, and the other after eating nothing. The researchers found that when the subjects ate nothing, they became fatigued faster and stopped exercising about 30 minutes earlier.
Dr. David Prince, an assistant professor of rehabilitation medicine at the Albert Einstein College of Medicine of Yeshiva University in New York, said that when you exercise on an empty tank, your body burns through stored carbohydrates first, then protein, before it finally moves on to fat. In the meantime, he said, "you lower your blood sugar, causing ravenous hunger that in most people would lead them to eat much more than they would otherwise."
His recommendation? A small piece of fruit, "just enough to give you energy for a more intense workout."
Keep in mind that he was talking about cardio only. Here's something else to be careful of:
"After a night of sleep, your spinal discs are filled with fluid, which makes them more likely to rupture if they're put under pressure first thing in the morning. Other joints and connective tissues could be more vulnerable in the morning because it takes longer to warm up and get the body's natural protective mechanisms working.
The best reason to exercise first thing in the morning, with or without food in your stomach, is if that's the most convenient time for you. Just do yourself a favor and warm up carefully, and don't do anything that would put your back at risk within an hour of waking. And if you're most concerned about fat loss, what you eat and do the rest of the day matters much more than whether you eat or don't eat before your workout."
Hope that helps with clarity.