Zinc deficiency can cause acne. Fatty acid deficiency can cause bumps on the backs of arms. I have also heard gluten allergies can cause bumps on the arms and milk allergies can cause acne. I have had bumps on my arms all of my life. If pinched they produce a small white pip ( like a seed). They don't produce the creamy white pus of a zit. Lots of lotion can reduce the bumps. When I was a child we asked the doc what I was popping out of my skin. He thought it might be the individual oil glands for each pore. On my fore arms a hair would be in the pip some times. Now after 40 years the skin an my fore arms is very dry and the hair does not grow all in one direction like it used to.