Even though they are much smaller, I still get bromide bumps when I sweat LOTS from mowing the yard. I believe bromide gets its name from the smell(?). Next time, smell that "oily and thick whitish yellowish stuff" (which sounds like bromide to me) and see if it also has a yucky smell...I would bet it's bromide.
As long as I still have fat reserves on my body (which I do), then I know I still have bromide just waiting to be released and passed OUT of my body.