hi...thanks for your query.
First i would like to mention that a wart
is a viral infection of skin.it is important to get that removed by a trained doctor by one of the several methods like electrocautery, cryo, lasers etc.Else it persists and gives rise to many more similar growths in the surrounding areas.A duct tape cannot remove it.
You have probably developed a contact allergy
to the adhesive material in the duct tape.You may apply a mold topical steroid
on it once daily for 5-7 days.It should subside .Have an oral anti-allergic to reduce the itching and avoid itching as this might spread the wart in the same area.
hope this helps..take care!