Given the data you provided (rash on the neck and on the back of the hands, several days after starting wearing new coat, previous history of environmental allergies to bees, pollen, mold, and dust), you might have experienced an allergic rash. The allergy is highly likely due to contact with a substance. The coat is quite suspicious because the areas of the body where the rash is located are exactly on the only places where the coat might directly come in contact with your skin.


You might want to visit a dermatologist fora visual inspection of the rash and additional allergy tests. Taking hydrocortisone and benadryl (generic name: diphenhydramine) is just what you need (corticosteroid to reduce the inflammation and antihistaminic to reduce the allergy itself) together with not wearing the coat at all. Avoiding exposure to other hyperallergenic substances for at least one week might be recommended.