Thank you for translating, ValiaSp.

But I have some suggestions of updates that can be done with this translation.

You who pass next to me and you not say my name -> You pass next to me and don't say my name
Only for giving me the idea that you exist -> Only to give me the idea that you exist
You sweared me that time soothes the pain -> You sweared to me that time can soothe the pain
Love save me from this idea about you -> Dear, save me from this thought of you
I want to exist even for me -> I want to exist for me as well
Search me find me make me feel your odor -> Search for me, find me, make me feel your smell

I'm not a fluent Italian speaker, if you wish you can request someone to proofread your text and see if there are more things that can be changed.

And what does "Missive" mean? I don't know this word in English, it would be better if you used a synonym.