Am I sinful, and is Ghusl obligatory for me if my clothes become saturated with the smell of perfumes and I pass by men?

A woman bathing to perfume herself before leaving her home is recommended (mustahabb) but not obligatory (wajib). Her work outside the home is permissible (ja'iz) if it is lawful (mubah) and free from religious prohibitions (mahadhir shar'iyyah) such as intermingling (ikhtilat), privacy with a non-mahram (khalwah), speaking in a soft and alluring manner (khudoo' bil-qawl), and ostentatious display of beauty (tabarruj).