Thanks for posting your query.
Clicking sound during swallowing may be due to temporo-madibular joint (TMJ
Do you have any past history of TM joint dislocation?
You should consult with ENT surgeon and should go for thorough check up.
You should also go for x ray
of TM joint.
Kindly stop performing clicking sound herself as this may cause damage in joint surfaces.
Dr. Mayank Bhargava