In what way is Iodine necessary for the immune system? It's major important function is in the synthesis of thyroid hormones. People with severe Iodine deficiency (which is not a huge problem in the United States, although mild, asymptomatic deficiencies occur somewhat frequently - still a small percentage of the population; if you're worried about it, eat iodized salt instead of kosher salt) are not immunodeficient or more prone to infections. Iodine deficiency produces mental retardation and hypothyroidism, not immunodeficiency (if you have a study to the contrary, I would be interested in seeing it)
However, TOO MUCH iodine IS immunosuppressive, and it suppresses the very parts of the immune system that you need to fight HIV (Cytotoxic lymphocytes, Th1 cells, and NK cells; here's one link: http://www.springerlink.com/content/xp0r26026tw32614/
If iodine is helful in fighting certain infectious agents (and there is very little data on this; I found one study on the use of iodine in fighting certain diseases of immunopathology), this is only because they are diseases where the immune response is the problem (e.g. tuberculosis: it is your immune response to the pathogen [Th1 cells activating infected macrophages, IFNgamma, TNFa, and to a lesser extent, CTLs] that is causing the granulomas [tuberculomas], scar tissue, and damage. Suppressing the immune system with large amounts of iodine might help here. Suppressing cell-mediated immunity in HIV would not help - it would actually be harmful, because the diseases have different mechanisms.
First, let me tell you how sorry I am to hear about your recent diagnosis. But I'm glad that you're feeling well! I should've said in my previous post about the lymph node that swollen lymph nodes due to HIV are usually (not always) "generalized lymphadenopathy" meaning that more than one lymph node is swollen. A single swollen lymph node may be a sign of a localized infection - e.g. an abscess, a tooth infection, an ear infection, dermatitis in your scalp, etc. Also if it's the size of a pimple, that's really small for a swollen lymph node. You should see your doctor, but it may not be due to HIV itself.
I would always be very careful about any cure that claims that all diseases (or symptoms) can be fixed by the same mechanism. Our bodies (and the pathogens that infect them) are pretty complex things, and its highly unlikely that any non-magical substance will be able to fix every infection, every immune defect, or every symptom. The immune system is one of the most complex body systems (not as complex as the nervous system, but right up there). HIV is also a very complex little pathogen. It takes a lot of study of immunology and virology to get a good grasp on how our bodies interact with this virus.
I wish you the best of luck. Keep us posted on any cures that you try, and how they work. I had a lot of friends try (and quite a few die trying) various cures back in the 80s and 90s, and even a couple more recently who weren't interested in antiviral drugs. As far as I can tell, the vast, vast majority of them are scams. They may not ALL be scams, but it's difficult to separate the good from the crap (since those selling crap dress them up as if they were legitimate, and even outright lie). I myself have not gotten good results with any natural cures, but I'll be very eager to hear if you manage to have success. I don't believe that there will be any treatment that will allow you to repeatedly test HIV-negative on an antibody test. There may be something out there that will help you to control the virus, though. Good luck! Keep us posted!
ps - what city are you in?