Think I may have carrot allergies. How can I tell--symptoms, tests, eetc?

Depends. True allergies and anaphylaxis are ige mediated reactions which means they cause hives, swelling, vomiting, serious breathing problems shortly after eating them. They can be tested by an allergist through skin & lab testing. Intolerances cause more GI symptoms of bloating, diarrhea, gas. Check this by eliminating the food for 2-3weeks & then reintroduce it. If you get the same symptoms, avoid.