Hi Jounaid,
I'm not sure what you mean when you say your hand "plucks the strings." If you're talking about when you change chords, your fingers touch some of the other strings, I think that is easily fixed if you just go a little slower, so you're training your muscles to do it the right way. I hope that makes sense.
As for you playing with a pick vs your fingers. I think that is ultimately up to you and the style you want to play. There are plenty of guitarists that don't use picks at all, and some who only use picks. I wouldn't worry about it too much, but just remember, some techniques and styles of guitar are a lot easier to play with a pick, and vice versa. It's good to be versatile!