I agree with bsmsl that you should take your 18 month old to a dermatologist. However I would not expect to find out the cause but you will get medicine to treat them. I have a 2 year old daughter who is constantly breaking out in hives and her dermatologist recommended using benadryl. It is very frustrating because we have been unable to find the reason why this happens. I would track eating habits and anything that your child comes in contact with that may help you narrow down the cause. Good luck.
Generally hives are coused by some sort of allergy, but there are other causes as well. I would recommend that you take you child to an allergist or a dermatologist for evaluation.