Is yours an onion smell specifically or just bad Body Odor ? Just from the pits?
I went to a dermatologist last Wednesday and she did a bacteria culture and a fungal culture of my armpits, meaning that she took one of those swabby things (excuse my simple language, I'm no doctor:) and took a sample of the bacteria under there to be shipped off and grown in a lab. This will hopefully see which bacteria are growing under there. For me, I also have an inflamed lymph node and inflamed hair follicles. Which is why I think that bad bacteria have grown under there and taken over. Since you also say that your bad smell is present even if you're armpits are "clean" and you are not sweating, I am thinking that you too have an overgrowth of bad bacteria/fungal infection. Again, I am no doctor. But this is just my hypothesis. I will tell you my results from the tests. I will get the bacteria culture one back hopefully tomorrow or the next day, and the fungal in three weeks.
We can get through this together! Just have faith. Everything happens for a reason, but you can overcome any obstacle if you never give up.