Cruciferous (lettuce) vegetables such as cauliflower, raddichio can have high levels of salicylate that can explain the itchy hives
that you are having. However, this is usually a secondary trigger for people with 'idiopathic' urticaria
(medical term for red, itchy hives that can feel swollen under the skin) and is occasionally generalised (i.e., whole body may be involved in hives).
I would not suggest going on a strict low salicylate diet as it is a very difficult diet but you might want to stop raddichio in your diet and start taking either cetirizine
10mg (max twice daily) or Allergra 180mg for the next 2-3 weeks until all the hives have cleared up. Sometimes the treatment needs to be continued for 3 months so check with your doctor on the right antihistamines.
If you do not high levels of salicylate sensitivity
(i.e., can tolerate other foods high in salicylates) then do NOT go on a strict low salicylate diet.
Sometimes in people with salicylate sensitivity, one may be able to tolerate some foods but not others in the 'high salicylate' list which may be the same with you.