You shouldn't use the passive form 잊히다/잊혀지다 after the object 너를. It should be an active form 잊다.
- 난 너를 안 잊을 거야 = 난 너를 잊지 않을 거야 = I will not forget you (I will intentionally remember you).
- 난 너를 못 잊어 = 난 너를 잊지 못해 = I can't forget you. (more of a natural state than intention)
- 난 너를 못 잊을 거야 = I think I can't forget you. (same, except it is weaker and more about the future).
- 너는 (내 마음에서) 잊혀지지 않을 거야 = You won't be forgotten (in my mind). * Note the different subject and no object.