Is there such a thing as general carbohydrate intolerance?

Diabetes? . Diabetes comes to mind. However I have a suspicion that your question is related to something else. If so, please describe your symptoms after eating carb.
Yes. It can be congenital, primary or secondary. Congenital: enyzyme defect at birth. Primary: enzyme defect develops over time (lactose intolerance). Secondary: caused by a disease or disorder (can sometimes be reversible).