Hand, Foot, and Mouth Disease (HFMD): This is a common viral illness that often presents with blisters or rashes on the hands, feet, and around the mouth, particularly in children. The recent vaccination could be a coincidental event, as HFMD is highly contagious and can be spread through direct contact with an infected person.

Allergic Contact Dermatitis: An allergic reaction to a component of the vaccine or another substance could cause skin blisters. However, the distribution on hands, feet, and around the mouth is less typical for contact dermatitis.
Erythema Multiforme: This is an immune-mediated condition that can be triggered by vaccinations, among other factors, and is characterized by target-like lesions, which could be mistaken for blisters. It often involves the hands, feet, and sometimes the mouth.

Stevens-Johnson Syndrome (SJS): A severe skin and mucous membrane disorder, usually a reaction to medication or infection. It can be life-threatening and requires immediate medical attention. While rare, the presence of blisters around the mouth and on the hands and feet, especially if accompanied by systemic symptoms like fever, should prompt consideration of SJS.
Toxic Epidermal Necrolysis (TEN): Similar to SJS but more severe, with widespread skin necrosis and detachment. It is a medical emergency.

Pemphigus Vulgaris: An autoimmune disease causing blistering of the skin and mucous membranes. It is rare in children and would be an unusual reaction to vaccination.
Bullous Pemphigoid: Another autoimmune blistering disease, which is rare in children and not typically associated with vaccination reactions.
Kawasaki Disease: Although it primarily presents with fever, rash, swelling of hands and feet, conjunctivitis, and cervical lymphadenopathy, the rash can sometimes appear as blisters. It's a rare condition but important to consider due to its potential for cardiac complications.