Is doxycycline a good drug against impetigo? will it work?

Not the best drug: Impetigo is a strep infection of the skin. Doxycycline might work, but isn't the best choice. But if your doctor prescribed it, she probably had a good reason, so take it as directed -- or contact her if uncertain. If you're doing this on your own (e.g. with leftover doxycycline), just don't. See a doctor to confirm the diagnosis and prescribe proper treatment.