Is it possible for joico k-pak smoothing balms to give you a headache?

Yes: In the field of medicine any and everything is possible , can be smell sensitive or chemical inhalation , treatment is stop it and inhale frehs air or cool steam inhalation may be ? Tylenol (acetaminophen). If no better see an M.D.

Hair Smoothing balm: I am not aware of headaches related to this smooth & straigthening balm. However, as Dr. Sinha stated maybe the coconut scent is an issues if you tend to be overlly sensitive to scents.