It's strange that some people keep mentioning sneezing. I don't get any involuntary reactions like this. I wonder what the cause of that could me. All my my reactions are people signaling to me (or others) that I smell - completely voluntary.
As far as deodorant goes, I have always had a difficult time with degree. Despite the fancy commercials about working better under stress, it's about the worst I've tried.
I did see a video (a couple of them) on youtube from people who have had very bad issues with deodorants not working and one said lemons were effective. The other wrote a long list of things to do, but she said Mitchum (unscented) with the oxygen technology was one of the better ones.
She also said she always uses an epilator and never shaves. I think it may take a while, but plucking the hairs out of your pits with an epilator or with electrolysis would be a good treatment for bromhidrosis. Those apocrine sweat glands can only leak through our hair follicles (pubic). So, destroying the follicles would stop the odor, since the sweat would not be able to escape. If possible, see if you can get your insurance to cover electrolysis for the treatment of bromhidrosis.