I reached puberty at the age of twelve, one month before Ramadan, and I started to observe Sawm (fasting) at the age of fourteen. Should I make up for the missed days of Sawm in these two years or not?
You should make up for all the days you did not observe Sawm in Ramadan after the age of puberty, whether continuously or separately. You should also repent and ask Allah for forgiveness, as you committed a sin by breaking your Sawm in Ramadan without a legitimate excuse. May Allah accept your Tawbah (repentance) and forgive you for your negligence. Allah states,
And all of you beg Allâh to forgive you all, O believers, that you may be successful
He also states,
And verily, I am indeed forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them, (till his death).