My daughter got a bad staph infection from just ripping off a hangnail. She was little, about three, so I did the mommy thing and put some neosporin on it and a Barbie band aid and a kiss. the next day I was putting a new bandaid on it and it was all red and yucky. I took her to the doctor because it really did look bad. The doc said it was a staph and she could have lost part of her finger. She told me to never put something like neosporin on a little cut like that and seal it up. I basically sealed in all the germs and kept it moist. She told me to wash a little cut or scrape with hot water and soap and that was it.
I do think that your environment might have something to do with getting staph or infections too. I have noticed that here where I live now it is very dry and seldom get any kind of infection. When we lived in a damper climate we all seemed to get them more.