Disclaimer:  Skin conditions can be very difficult to diagnose by words alone (at least for me).  Don't forget that a picture can be worth a thousand words, not that I'm recommending you post one.  Just that it might be easier for your family physician to make the diagnosis.

With that said, white bumps make me think of abscesses (pus pockets), folliculitis, acne (pimples), etc.  However, these are usually painful.  Folliculitis is common in those w/lots of visible body hair, especially if they shave.  

But if there's no pain, then I think of keratosis pilaris which is common on the backs of the arms and on the thighs, too.  Some over-the-counter exfoliants can help fix this.

If it's a painless white flat rash rather than a raised white bump, then I might think of tinea versicolor.  This is typically present in sun exposed areas.  What happens is that the skin gets infected and loses its pigment cells.  As long as there's no sun exposure, you can't tell anything's wrong.  However, with sun exposure (perhaps you were shaving in anticipation?), health uninfected skin darkens (tans) while the infected skin stays light (white).  Simple anti-fungals can treat this.

Molluscum contagiosum is a skin (white) colored bump caused by a virus.   Sometimes cheesy white material can expressed from the middle.  It can be spread by scratching (or shaving).  You can treat it via mechanical means or just wait it out.

Bottom line, go see your family physician.  Good luck!