Actually, this isn't terribly uncommon. During intense exercise your body can begin to burn amino acids (protein) for energy, especially if you have depleted carbohydrate stores. When your body burns amino acids, it produces a number of chemicals and compounds that have to be flushed from the body. Urea - a form of ammonia -- is one of those compounds.
Under normal circumstances, your body excretes urea via urine. However, if you are producing a lot of it (for example, during intense or long-duration exercise), your body can also excrete urea via respiration (through your lungs) or in perspiration. This can result in an ammonia scent in your clothing, sweat or even in your nostrils.
Diet can have some impact on this. If you are low on carbohydrates, this can encourage the body to turn to protein for fuel -- thus producing more urea. Also, if you don't have enough or too much dietary protein, you can experience a similar result.
Try eating a meal one hour before you work out that has plenty of complex carbohydrates (like oatmeal) as well as at least 20 grams of lean protein. Whey protein or a whole food source such as skim milk or chicken breast are all good choices.
Also, be sure you are frequently washing your workout clothing. The urea can build up (especially in cotton) and seem much worse than it is. Consider some moisture-wicking clothing as well. I like Under Armor Heat Gear.
Finally, if this persist more than a few weeks, just to be safe, see your doctor. Excessive urea excretion from perspiration and respiration can be a sign of more serious conditions, including diabetes and kidney disease.
Best of luck!