I can't say that I've ever heard of someone being allergic to all carbs in general, although many people do have true food allergies, but I have heard of many people who are carb intolerant which simply means that your body doesn't like them and responds to them by making you feel bad in a variety of ways (tired, indigestion, diarrhea/constipation, aching muscles and joints, etc...).
Insulin resistance is when you have had too much insulin in your bloodstream for too long, usually as result of a diet that is high in high glycemic carbs or just plain too high in carbs in general, and after a while the cells of your body become "immune" or resistant to the effect of the insulin causing your body to need more and more insulin to do the job that less once did. This is often referred to as Syndrome X, which has a variety of symptoms including, but not limited to, high blood pressure, obesity, high triglycerides, high LDL and low HDL. Too much insulin can also aggravate inflammatory conditions by driving eicosanoid production in the wrong direction. A blood test that meaures how much insulin you have in your bloodstream would be the best way to diagnose insulin resistance along with the presenting symptoms.