Short Answer
Using hair regrowth products such as shampoos, vitamins, or other chemicals is allowed as long as they are not harmful.
A hair transplant is a type of surgery that moves hair you already have to fill an area with thin or no hair. This is allowed since hair would normally be on your head in that area, so it is correcting a defect.
It is forbidden to use real human hair as a wig or as hair extensions, because human hair is sacred and forbidden to be used as adornment. This is the case even if someone’s hair has fallen out as a result of illness. It is allowed to use animal hair or synthetic hair as a wig or as hair extensions.
What the Qur’an and Sunnah Say
A’isha narrates that an Ansari (Madinan) girl was married and became sick, so all her hair fell out. They (her family and friends) intended to connect her hair with false hair, so they asked the Messenger of Allah who said: “Allah has cursed the woman who joins her or someone else’s hair (with the hair of another person) and the woman who asks for her hair to be joined.” (Bukhari #5590)
What the Scholars Said
A group of scholars said, “It is fine for a woman to put the hair of a camel or a goat in her hair strands.” (Al-Fatawa Al-Hindiyya 5:358)
Advice
Keep in mind that if the wig is not detachable then it is considered your actual hair and you may wipe over it or wash it for wudu and ghusl. If it is removable, you must must remove it when purifying yourself.
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Shaykh Mustafa Umar