There are two possible causes for a dry and itchy scalp in this situation. A detailed scalp evaluation is required to understand the specific cause in each case.

Minoxidil is a solution prescribed for hair fall. It is mainly used for androgenetic alopecia and female pattern hair loss. The use of minoxidil can produce some side effects and should be used as prescribed by a dermatologist.

Minoxidil can cause irritation and dryness of the scalp. This can present itself with itching and white flakes that can be mistaken for dandruff. In this case, a strong clarifying shampoo can help clear product buildup.

Secondly, seborrheic dermatitis can also cause flaking and itching. In this case, an antifungal shampoo can be used to treat. Additionally, you may require added creams that a dermatologist can prescribe to you.

The treatment may include a change in shampoo or additional use of a cream or lotion to control the dryness. It is advised to consult a doctor rather than self-medicating. Dandruff also increases hair fall. So, it is best to start treatment at the earliest.

References:
Badri T, Nessel TA, Kumar D D. Minoxidil. [Updated 2021 Dec 19]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2022 Jan-. Available from: https://www.ncbi.nlm.nih.gov/books/NBK482378/