If the lesion over genital area is Lichen sclerosus
atrophicus, then the mouth problem does not seem to be related to it.
But Lichen planus
can involve both genital area and tongue. Though itching is a symptom of lichen planus, in mouth it can lead to burning. Metallic or bitter taste have not been reported as the features of lichen planus.
You have visited a dentist
and a gynaecologist. I suggest you to give a chance to dermatologist
Dr. Ajit Singh Kulhari
MD - Skin & VD