Post-treatment itching is usually a sign you are about to get ingrowns. Doing heavy exfoliation and generous use of moisturizer can often help reduce itching and ingrowns.
If you itch immediately after, do not scratch, but instead cleanse the area with witch hazel and then use a thin coat of antibiotic ointment or antihistamine cream like Benadryl. Scratching and rubbing the skin can lead t infections or worse itchiness.