The sap and crushed leaves contain a chemical which is absorbed by skin cells. The body mounts an immune response to these contaminated cells. Once begun, the reaction ends only when all the contaminated cells have been shed. This is one argument for scratching as much as possible, at the expense of additional scarring. There are a lot of conflicting suggestions for treatment.
Antihistamines are either very effective or worthless.
If the affected area is small enough, self treatment with over the counter remedies can provide 'temporary relief'. One person reported losing a lot of skin with this method. Others report that the itching recurs worse than before, possibly due to increased blood flow in the area. I did not try this method. This is reputed to cause cracking and even more itching.