Allergic Contact Dermatitis: This is the most likely diagnosis given the history of application of nail polish followed by the development of a blistering pruritic rash around the fingernails and toenails. The rash persists despite removal of the nail polish, which is consistent with an allergic reaction to one of the components in the nail polish, such as toluene sulfonamide formaldehyde resin, formaldehyde, or dibutyl phthalate.

Irritant Contact Dermatitis: Although less likely than allergic contact dermatitis given the delayed onset and persistence of symptoms, irritant contact dermatitis could occur if the nail polish or its remover caused direct irritation to the skin.
Phototoxic or Photoallergic Reaction: If the nail polish contains certain chemicals that become active or allergenic upon exposure to sunlight, this could be a consideration, especially if the symptoms worsen with sun exposure.

Erythema Multiforme: A severe skin condition that can be triggered by various factors, including infections and medications. It's crucial to consider this diagnosis due to its potential severity and the need for prompt treatment.
Stevens-Johnson Syndrome/Toxic Epidermal Necrolysis: Although rare, these are life-threatening conditions that could be triggered by an allergic reaction to certain chemicals. Early recognition is critical for management and prevention of severe outcomes.

Psoriasis: Could be considered if the rash has characteristic psoriatic features, although the direct temporal relationship with nail polish application makes this less likely.
Dyshidrotic Eczema (Pompholyx): Characterized by small, itchy blisters on the hands or feet, but it's not typically directly associated with the application of nail polish.
Autoimmune Bullous Diseases: Such as pemphigus or pemphigoid, which are rare and would require specific diagnostic testing for confirmation.