Final answer:
The condition described is complicated cellulitis, as the infection has progressed and is accompanied by additional symptoms.
Step-by-step explanation:
In this case, the swollen red arm with vesicles containing pink or purple fluid and purplish skin around it is indicative of a complicated cellulitis. Cellulitis is an infection that affects the dermis and subcutaneous tissues. Complicated cellulitis refers to severe cases where the infection has spread or is accompanied by other symptoms such as necrotizing fasciitis.