It is permissible for a Muhrim to shave his head if there is a problem, but it is obligatory to offer a Fidyah for shaving it, and Clarifying what the Fidyah is Sahih Muslim 1201 b
Arabic hadith text
حَدَّثَنِي عَلِيُّ بْنُ حُجْرٍ السَّعْدِيُّ، وَزُهَيْرُ بْنُ حَرْبٍ، وَيَعْقُوبُ بْنُ إِبْرَاهِيمَ، جَمِيعًا عَنِ ابْنِ عُلَيَّةَ، عَنْ أَيُّوبَ، فِي هَذَا الإِسْنَادِ . بِمِثْلِهِ
Translation
This hadith is narrated on the authority of Ayyub.