I wish I was a doctor and had an answer for you. Unfortunately, I'm looking for an answer to a similar question. I have white bumps on the tops of my feet, mainly toward the outer half/ankle, and a few around my Achilles. The only things I've ever considered were warts/fungus from gym showers, or damage from severe sunburn I got on both feet when I was 14 during a church car wash on asphalt all day. I put my feet in buckets of ice that night and had to use Aloe Vera gel for weeks. I figure I have some damage from that, but I've asked both my primary care doctor and a dermatologist and they both just said "that's nothing to worry about.". I hate that. That's not an answer. I've tried anti-fungal creams, wart removers, and even pedicures. No luck.
They're different sizes, but small nonetheless, and for me they don't generally itch. If I do scratch the top of my foot, I sometimes scratch some of the tops of the bumps off. They appear to be like dry skin (at least the tops), and my feet have been dry since I was very young (I'm 29 - male). If I scratch them off or scrape them when I'm using a foot file that I use regularly on my heels to prevent cracking & bleeding, the spots/bumps come back. If I get any sunburn/tan, the spots show through staying white. I have no idea what to do.
Good luck to you