It sounds like you were trying to keep your voice down while you were singing, maybe because there was other people in the house, or trying to sleep. I do that, so what you should do if you're unkeen on letting people hear you whilst recording, wait until you have the house to yourself, or just go nuts, and belt it regardless. It has a good vibe with it. I'm really digging it, it sounds quite like a song on Please Please Me, I can't think what though. "Baby it's You"? The guitars are brilliant, and your voice isn't bad!
I think this is a really good composition though, I'm a sucker for Beatlesesque stuff. All it needs is an oomph with the vocals, even just double tracking them, and it'd be sorted.
You've got the John and George stuff down to a Tee, so you should give Paul and Ringo a phone, and you'd pretty much have the full Beatles instrumentation back. Great job!