Can tb neck lymphadenitis damage fallopian tubes? is it possible for tb lymphadenitis to spread to genital organs?

Rare: It is possible but not common especially if you have been diagnosed and are being treated.

TB: Can affect the pelvic organs. Matter of fact it is one of the causes for infertility in females in third world countries. Treatment with medicines is effective. See a good infectious disease doctor. If you are in India , most of the GPs or gynecologists are able to take care of this problem if you can't find a specialist.