In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Answering your question, Sheikh Kifah Mustapha, the Imam and Director of The Prayer Center of Orland Park and representative for Dar El Fatwa of Lebanon in the US, states:
Yes, it is allowed for Muslims to use hair gel that contains alcohol. Alcohol is forbidden to be consumed because it is an intoxicant.
However, it is not forbidden that alcohol touches the body because it is pure made from pure originated items like grapes, dates, rice or barely.
Almighty Allah knows best.