I can very much relate to what you said about not trusting the people you ask to tell you the truth about whether or not you smell. I've asked a few people straight out (Haven't had the guts to put the question to strangers like you have, though...) and every one of them tells me that they don't smell anything. And yet, everyone else's body language and mannerisms tell me that they do. It's hard to envision what being in public would be like without the smell, but I'll definitely be paranoid even when it's gone (if it ever goes away). Unlike you, I never smell myself, because I've never been able to detect the odor to begin with.
I think it's interesting what Aluna said, about the time that you thought that you could smell it. For the past year, I've gotten this musty, nauseating smell in my nose on and off during the day. I don't believe I have a sinus infection or any such thing (if it was, I'd probably have headaches, congestion, and, eventually, severe sickness to go with it), so perhaps that's what the odor is. Taking that odor into consideration, I can certainly understand now why people would react so strongly to it (coughing, sneezing, and sometimes seeming on the verge of vomiting)!