I have a bacterial skin infection on my chin & mouth area, also spread in some areas of neck nd chest. is it normal for it to itch after applying the?

Yes: Itch associated with the topical infection is a common symptom. Continue to apply the medication as directed by the physician. This will improve when the infection starts to improve. You could ask your doctor if an oral antihistamine is safe to help with the itchy skin and ask exactly which is safe. Don't just buy one and start treating yourself.