Is it permissible for a sister to remove her hijab if a doctor advises her to do so due to a skin disease on her scalp?

Your sister is not permitted to remove her hijab based on what the doctor mentioned. The necessity that allows what is forbidden must be confirmed as genuine by trustworthy doctors, and that the harm cannot be averted except by removing it. It is unlikely that the hijab would be harmful to the scalp. A reliable consultant doctor specializing in skin diseases has stated that the hijab does not negatively affect skin diseases of the scalp. However, the type of fabric of the hijab might have an effect, and in that case, it should be replaced with another fabric.