Büsbütün unutuyorum seni, maziye karışiyor şimdi yeminim, icimde sana karsi olan kin bile eskisi kadar yok, anliyacagin sende herkes gibi oluyorsun yavas yavas

My attempt as a learner

Büsbütün unutuyorum seni,

I am completely forgetting you

maziye karışıyor şimdi yeminim,

I swear now he/she is meddling in the past

içimde sana karşı olan kin bile eskisi kadar yok, anlayacağın

deep inside me I am the one opposite to you, even though there is not as much resentment as before, you will understand

sen de herkes gibi oluyorsun yavaş yavaş

You too, are becoming very slowly like everybody else 

Wait for native speakers to correct, as some words have several possible meanings. 

I am entirely forgetting you, my swear is now interfusing to past, even the hatred in me for you is not much as before, you are slowly being like anyone else. 

 I am completely forgetting you, my oath is now becoming part of the past.

my try at that bit