I looked up Effexor in my PDR and thyroid complications are not listed. I would say they are unrelated. As for a study... most studies are done to test a new drug or a new use of a drug. It is extremely unlikely that any study is being done on cysts on thyroid. Perhaps you can go to a free clinic for help.
You don't say why you stopped the Effexor. Is it because you feel you don't need it now, or did a doctor advise you to stop?
You say you are easily irritated, and this could be due to depression, as it is one of the symptoms.
I have been on Effexor for as long as you, and have not had trouble with cysts, but we are all different. Do you think they are due to taking Effexor? Did a doctor tell you this was the case?
If you want to participate in a study, I think you will have to consult a doctor about this.