Hello! I don't think you're too young to be gloomy in my opinion. I think it's a fallacy for people to think that youths are all vitality and joy. Okay, I'm digressing. Anyway, a few things to note. The title: The Letter that was not Sent would probably be more grammatically correct.
And as for the poem, I think you need to be careful of your usage of thee, thou, thine and thy. They're pretty easy to mix up. Each refers to a person's specific relation to an object/person. Hmm, if I'm remembering correctly, 'thy' should be an actor's relation to an object i.e. Thy heart/sword. So an easy way to remember it is that it's similar to my, kinda like an older form of the word.
So for the First Stanza, Soon I shall leave thou, should be Soon I shall leave thee,
For the Second Stanza, I'm a bit confused myself if the 'Thy' in Thy might hate me should be 'Thee' or 'Thou', but I'm pretty sure it's either one of these two.
Easy way to remember is (very roughly) : thy -]my, thee/thou -]you, thine -] your(kinda)
Hope I'm not overly wordy, and I hope that helped if you ever want to use old English again. (: Cheers.