Hereditary Hemorrhagic Telangiectasia (HHT): This condition is characterized by recurrent epistaxis, telangiectasias, and an increased risk of arteriovenous malformations. While ichthyosis is not a primary feature, the combination of recurrent epistaxis and potential skin manifestations could align with HHT, especially if there are other systemic signs.

Atopic Dermatitis with Associated Conditions: Atopic dermatitis can sometimes be associated with ichthyosis-like skin changes. Recurrent epistaxis could be related to allergic rhinitis or other atopic conditions that often coexist with atopic dermatitis.
Keratosis Pilaris and Allergic Rhinitis: Keratosis pilaris can present with ichthyosis-like skin changes. When combined with allergic rhinitis, which can cause recurrent epistaxis, this could be a plausible diagnosis.

Wegener's Granulomatosis (Granulomatosis with Polyangiitis, GPA): Although less common, GPA can cause recurrent epistaxis due to nasal granulomas and vasculitis. Skin manifestations can sometimes resemble ichthyosis. Missing this diagnosis could be fatal due to the potential for severe organ involvement.
Sjögren's Syndrome: This autoimmune disorder can cause dry skin (potentially resembling ichthyosis) and is associated with an increased risk of lymphoma. Recurrent epistaxis could be a feature of associated nasal dryness or vasculitis.

Netherton Syndrome: A rare genetic disorder characterized by ichthyosis, atopic manifestations, and an increased susceptibility to atopic diseases. While not directly associated with recurrent epistaxis, the atopic component could indirectly contribute to this symptom.
Fabry Disease: A lysosomal storage disorder that can cause skin manifestations (including angiokeratomas that might resemble ichthyosis in some cases) and vascular dysfunction leading to potential epistaxis. It's a rare condition but should be considered in the differential due to its systemic implications.