What is the most likely reason for clicking in my throat when I swallow?

Ear clicks. The most likely reason for clicks when you swallow is the opening and closing of the eustachian tubes. They go from the back of your throat to your ears. When you swallow or yawn, you open the tubes and equalize the pressure to your ears. Sometimes ear or throat infections can make this worse. It would be good to check with your doctor.
Uncommon complaint. but clicking throat is a surgically treatable problem. See an ENT for consultation.
Thyroid cartilage. Probably an unusual anatomical variant of "voice box' cartilage. See ENT doc. http://ucdvoice.org/wp-content/uploads/2013/11/Clicking-in-the-throat.pdf.