Hypochondriacs and Germaphones: Do you wash your hands after petting a dog?

My family has finally adopted that Papillon I asked a question about a while back.

Cappuccina I didn’t choose this name is a wonderful dog who is very affectionate and loves to be petted and rubbed. However, being the OCDish hypochondriac that I am, I can’t help but feel the need to wash my hands every time I touch her. As she grows more accustomed to our family and seeks our attention, she is getting touched more and more often and the hand washing is getting a little out of hand.

Am I being a little nutty with my hygiene? Anyone else act similarly with their pets? If you got over it, how? If not, how important is it to get over it?