History of exposure to rat: This would be relevant in cases of diseases like leptospirosis, but not typically in this scenario.
History of exposure to cat: This is the correct answer. Exposure to cats is associated with cat scratch disease (CSD), caused by Bartonella henselae. It often presents with a blister at the site of the scratch or bite, followed by axillary lymphadenopathy.
History of similar complaint in family members: This would be relevant for conditions with a genetic predisposition or familial pattern, such as in autoimmune disorders, but it is not typical in CSD.
History of tick bite: This could suggest diseases like Lyme disease or other tick-borne diseases, which usually present differently and not with a blister at the site.
Thus, the correct answer is History of exposure to cat (2) because cat scratch disease is commonly associated with these symptoms.