I had exposure to syphilis. 20 days later, i started azithromycin 1g followed by doxy 100mg bd dose. on 10th day of doxy course, if i shared a cigarette with someone when i had a very small stomatitis on lower lip, have i exposed her to syphilis?

No. You had to have a syphilitic ulcer on the lips and the cig. sharer too.

See comment on your duplicate question, answered by Dr. Grim. It is not possible to develop a syphilitic lesion while taking doxycycline. Within 2-3 days of starting doxycycline (and maybe azithromycin), you were no longer able to transmit syphilis, even by sex. Something else caused the "stomatitis", maybe an oral herpes outbreak. Neither herpes nor syphilis is transmitted by shared cigarette.