All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible for you to delay making up the fasts until after the coming Ramadan due to hardship. Allaah is merciful to His slaves and He does not overburden them with anything they cannot endure. Allaah says (what means): {Allaah does not charge a soul except [with that within] its capacity.} [Quran 2:286]
Therefore, you should hasten to make up what does not consist in hardship for you, and whatever you find difficult to make up now, you may delay it until after Ramadan.
Also, since you were unaware of the obligation of making up the fasts before the beginning of Ramadan, then you are not obliged to pay the compensation (Fidyah) because of the delay in making up the fasting of those years.
Ibn Hajar Al-Makki said in Tuhfatul-Muhtaaj: "Al-Athra‘i said: 'If one delays making up fasts due to forgetfulness or ignorance, then there is no compensation, as understood from the statements of the scholars'; and what he means is ignorance of the prohibition of delaying the fasts, even if one mixes with learned people, because this is a subtle matter." [End of quote]
For more benefit, please refer to Fataawa 116161 and 95501.
Allaah Knows best.