Keratosis Pilaris: This condition is characterized by small, hyperkeratotic papules that can be itchy, often appearing on the arms, legs, buttocks, and cheeks. The description of small dots, hyperkeratotic skin, and itchiness matches the clinical presentation of keratosis pilaris.

Pityriasis Rosea: Although typically presenting with a herald patch followed by a wider rash, some cases can start with isolated, itchy, hyperkeratotic lesions. The size and itchiness could fit this diagnosis, especially if the patient is in the early stages.
Eczema (Atopic Dermatitis): Eczema can present with hyperkeratotic lesions, especially in chronic cases, and is often accompanied by intense itchiness. The description could fit a localized form of eczema.
Lichen Simplex Chronicus: This is a condition where chronic scratching leads to thickened, hyperkeratotic skin. If the lesions are itchy and the patient has been scratching them, this could be a possible diagnosis.

Basal Cell Carcinoma: Although less likely given the description of multiple small lesions, basal cell carcinoma can occasionally present as a small, hyperkeratotic lesion. It's crucial to not miss this diagnosis due to its potential for local destruction if left untreated.
Squamous Cell Carcinoma: Similar to basal cell carcinoma, squamous cell carcinoma can present as a hyperkeratotic lesion and must be considered, especially in sun-exposed areas or in immunocompromised patients.

Phrynoderma (Toad Skin): A rare condition characterized by hyperkeratotic papules, often associated with nutritional deficiencies or environmental factors. It's less likely but could be considered if common diagnoses are ruled out.
Darier's Disease: A rare genetic disorder that can present with multiple small, hyperkeratotic papules. It's an unlikely diagnosis but should be considered in the appropriate clinical context, especially with a family history.