why is "esquecê" not in infinitive form?
The verb loses its ending when you merge it with the pronoun.
"Eu não posso esquece-la" means "I cannot forget her".
So, "consigo" should give a sense of "managing to / being able to forget her" So, I think, "I just cannot forget her" is a better translation.
If I use "posso" instead of "consigo", how would that change the connotation of this sentence?
It could give the meaning of "I shouldn't forget her".