Final answer:
For the burn patient with allergies to penicillin and sulfa-drugs, silver sulfadiazine is contraindicated due to its sulfa drug composition. The other listed medications do not pose a known allergy risk based on the patient's profile.
Step-by-step explanation:
A patient coming to the clinic with a hand burn that is red, painful, and has a small, unruptured blister should be assessed carefully especially when knowing their allergies. Given the listed allergies particularly to penicillin and sulfa-drugs silver sulfadiazine is contraindicated because it is a sulfa drug, and there is a risk of an allergic reaction.
The other medications listed, such as mupirocin (Bactroban), azithromycin (Z-pack), and clarithromycin (Biaxin) do not fall into the categories of drugs to which the patient has known allergies and thus are not contraindicated based merely on the patient's allergy profile.