Since it's in the form of quoted speech, we don't know who "I" is. However, with the comma before it "Nora Jane" is most likely a form of address, meaning whoever is speaking is speaking to Nora Jane. (There's a vague possibility it's intended to be a signature, but that would be pretty ambiguous.)
In other words, assuming the most likely scenario (that the speaker is addressing Nora Jane), we don't know who is doing the loving, but Nora Jane is the one who is being loved. The person who loves Nora Jane could be her mother, brother, lover, or friend. Since you say it's written from a "boy's" perspective, he's probably supposed to be the one doing the talking (and the one who loves Nora Jane).
You can read more examples of direct address here: https://www.thoughtco.com/direct-address-grammar-and-rhetoric-1690457