If I am currently an Oathbreaker, is it possible for my character to repent for his sins in some way and choose a new a subclass(like redemption) or not?
Ask your DM
Page 97 in the Dungeon Master's Guide defines the Oathbreaker. It also has an inset titled "Oathbreaker Atonement". It starts off with
If you allow a player to choose the Oathbreaker option, you can later allow the paladin to atone and become a true paladin once more.
And later continues with
(With your permission, the player can select a different deity or sacred oath than the character had previously.)
The last sentence is the caveat
A paladin who breaks his or her sacred oath a second time can become an oathbreaker once more, but can't atone.
So, yes, provided your DM allows it and your Paladin hasn't Fallen twice. You and your DM should both definitely read that inset before proceeding.