The way I explain how to wear finger picks is: "you pick the strings with your finger tips; but you happen to have a metal pick inbetween your finger tips and the strings".  

The pick is made up of two parts -- the band that holds the pick on the finger and the metal extension pick that comes off the band and covers your fingertip. If you are picking with just the metal pick part then you are putting all the tension on the band that is around your finger, and it will wear into your finger after a while and hurt it.  I like to put the picks on the fingers to where I can feel my finger tip pushing on the back of the metal pick part that comes off the band. The metal pick should be curved to the same contour of your finger tip so that you can put the pick on the finger and push against the backside of that metal pick. So you will need to put the band up on the finger more so and now you are picking with your finger tip and putting the pressure on the pick and not the band.