I can't think of any allergy that would be triggered by ice... after all, it's just frozen water. I think the itching is nerves on your tongue that have been numbed by the cold finally thawing out enough to "complain" about it!
There are two reasons that can make it itch and one is, if you have a daily products allergy. The second reason is that your tongue is sensitive. I think your tongue is sensitive and it may have been cause by eating a lot of ice or taking hot drinks. You should consult a doctor for advice.