If people think this is bad I can bet you that some other things you touch on a daily basis like doors, the bathroom sink handles if they don't have the touch-free fixtures, the elevator buttons at the office, etc. are probably even worse than the shopping cart handles for what is on them. As long as you are washing your hands and keeping sanitary enough throughout the day you'll be fine. My wife is addicted to hand sanitizer and Wet Wipes while I hardly use the stuff. I don't get flu shots either while she does and the most I had was a head cold this winter while she probably had the flu and a really bad cough at least once. I think your body needs to build up some kind of immunity.
I can't find the link to it right now but my dad sent me something that research showed that hand sanitizer is effective for X ammount of time after you apply it and that you don't need to continue reapplying it over and over each time you are paranoid you just touched something with germs. The skin on her hands sometimes looks irriated because she probably uses the stuff too much, I had her try to start using that Gold Bond sanitizing creme versus using that liquidly alcohol based stuff most people use and I think that stuff is less irritating to the skin and does the same thing.