Well, "pet rock" is a pretty dated image, and if you're really only 29, one that's way before your time. It may be a perfect metaphor for what you're trying to say here (if I'm reading it right," but it's still pretty dated. Maybe this would work better in third person; tell us a story about somebody who had a pet rock. That way it doesn't matter if it's such a dated image; the singer isn't trying to pass it off as a story that's happening right now in 2012.
The idea that is really interesting here is the image of somebody who is, umm, under some sort of care for some sort of, umm, mental disorder, who realizes that "if I DID have a pet rock and I started talking to it, they would take it away..." Someone who needs to have a different sort of "friend" than the typical "normal" person, but who knows that if they try to have that sort of friendship, it's just going to be seen as "wrong" ty "them." Especially for Aspies and others on the spectrum, this is a HUGE issue - I know what would help me feel better, but I also know it would be perceived as something else wrong that I'm doing. Just capturing the instant when the singer is feeling this conflict.
(I do a lot of critiquing of song lyrics, so I do tend to focus in on this sort of grammatical and wordsmithy stuff, don't take this personally)