You didn't mark this into sections (you know, like verse, chorus, etc), and I'm not clear on how you see this fitting into a musical setting. You start with the two rhyming lines that work--they go together in a rhythm that's compatible for the purposes of setting to music. Then the lines get shorter, so the music rhythm would have to adjust. Your rhyme scheme continues, so you have AABBCC for the first six lines. Rhythmically, though, those six lines read more like four lines. Unless, like I mentioned, you change the rhythm of the song when you get to line 3.
So let's call the first six lines the verse and set them aside for the moment and look at the next six lines. The first five are short and the last one is long, and the rhyme scheme has changed to, well, actually, I don't think there is one. Would this be verse 2? It isn't likely to fit well into the same melody as verse 1 and the rhyme scheme doesn't match, so I don't think so. So, let's call this the chorus.
Now the last seven lines. They don't match either the verse or the chorus (remember, I'm just assigning titles so I can analyze the song--they may not agree with how you intended), so let's call it a bridge. The rhyme scheme is AAABBAA. The rhyme scheme, the number of lines, and the uneven rhythms of the lines are unbalanced. This is okay, because the theme of this lyric is very unstable and everything about your lyric strongly supports an unstable theme. Ha! You thought I was going to say it was all bad, didn't you???
As far as suggestions for possible improvement. You could make it more dynamic (and less passive) by changing a few words a little. For instance, you could change:
with a slam of a door
you were here no more
Since you'd be gone
I had to learn to be strong
to something like:
You slammed the door
I fell to the floor
And I knew you were gone
So I had to be strong
The part I called the chorus is pretty wordy, which, I think, weakens it. Maybe it could be tightened up to make it stronger. Maybe something like:
I've heard no one loves like a mother
But you showed me that isn't true
And, no, you can't come back home
Because the damage is done
I've lived far too long on my own.
These are just some ideas based on my own understanding of songwriting and what you're trying to say. Feel free to ignore me completely. And, if anything here is helpful, feel free to use it as you wish.
Vicki