At the starting of haydh(since puberty), I didn't know about the fact that fasts are wajib , and we have to make their qaza before the next ramazan. So now I am trying to cover all my qaza fasts. Am I doing right?

Yes, you are doing right. If you didn't know it is wajib to fast, along with fasting the qadha, you have to pay kaffare e takhir that is 750 grams of food (wheat, barley, bread or suchlike) to a poor person for every fast missed.