The incorrect option would be b. Topical antibiotic preparation.
Topical antibiotics are not appropriate for the treatment of fungal infections like the one that Paul currently has. Oral antifungal medication, and continuing with the topical antifungal applications both remain good options, and educating Paul again regarding not sharing personal items would also be necessary to ensure that this condition doesn't spread to others. However, it would not be advisable to prescribe a topical antibiotic to Paul at this stage, as it would not be effective in treating his condition, which is fungal in nature.