I believe the bumps you are referring to are Fordyce spots. A dermatologist should be able to tell the difference between the two right away. I really doubt you could have transferred the warts on your hands to your genital area. Certain strains of hpv are responsible for warts in certain places. The strains responsible for warts on hands are programmed to cause warts on hands and the same is true for strains causing genital warts. Here are a couple links regarding Fordyce spots:
http://en.wikipedia.org/wiki/Fordyce%27s_spot
http://www.visualdxhealth.com/adult/fordyceSpots.htm
Warts in general are highly transmissible, so I think it's certainly very likely that they could have transferred from your hand to your genitalia.
Thing is, the only actual difference between genital warts and regular warts is that genital warts only occur on the genitalia, so you should still probably seek treatment and inform your partners.
Good luck!