Seborrheic Dermatitis: This condition is characterized by inflammatory patches with overlying dry skin, often on the scalp, and is common in adolescents. The absence of hair loss also supports this diagnosis, as seborrheic dermatitis typically does not cause significant hair loss.

Psoriasis: Although psoriasis can cause hair loss, it often presents with dry, scaly patches on the scalp without significant hair loss, especially in its early stages. The age of the patient and the description of the lesions make psoriasis a plausible diagnosis.
Eczema (Atopic Dermatitis): Eczema can manifest on the scalp with dry, inflamed skin and is common in adolescents. While it can sometimes lead to hair loss due to scratching, the primary complaint here is inflammatory patches with dry skin, fitting the eczema profile.
Contact Dermatitis: This is a reaction to something that has come into contact with the skin, such as hair products, which could cause inflammatory patches and dryness on the scalp. The lack of hair loss is consistent with contact dermatitis.

Tinea Capitis (Ringworm of the Scalp): Although the question specifies no hair loss, early stages of tinea capitis can present with inflammation and scaling without significant hair loss. It's crucial to consider this diagnosis due to its potential for spreading and the need for antifungal treatment.
Discoid Lupus Erythematosus: This condition can cause scaly, inflamed patches on the scalp and can lead to scarring hair loss if not treated. Early detection is critical to prevent long-term damage.

Keratosis Follicularis (Darier's Disease): A rare genetic disorder that can affect the scalp, causing dry, crusty patches. It's less likely but should be considered if other diagnoses are ruled out.
Lichen Planopilaris: An inflammatory condition that can cause patches of hair loss and scalp inflammation. While it's less common, especially in adolescents, it's a consideration in the differential diagnosis due to its potential for significant hair loss over time.