I've been paying attention to information about hormonal therapy, including Lupron, for a dozen years now, and I have never heard of head cold and allergy symptoms being associated with Lupron or any aspect of androgen deprivation therapy.
Here's my personal experience. Lupron has been the foundation of my intermittent triple blockade program, and I have been on Lupron for a total of 69 months, intermittently, starting in December 1999. During that time I usually experienced one or two colds a year, sometimes none; I seemed to be healthier than my coworkers. I have been under allergy treatment for decades - long before I was diagnosed. My allergies got no worse during the Lupron treatment periods. In fact, I was able to stop getting injections and switch totally over to medication perhaps a half dozen years ago.
If you come across any solid information that there is a connection between Lupron and such symptoms for some patients, please bring it to the Board.
Have you considered a food allergy as the cause of your symptoms? That might explain the on and off aspect.
About the hot flashes, what are you doing to counter them? Are you familiar with countermeasures that often help?