No, obsession is a sign of abnormality.
I suspect you're quite young and maybe what you call obsessed is really crushing on someone.
You're crushin' and it's all them hormones in your body.
You are young, you will probably grow out of this.
If it was normal they wouldn't call it being "obsessed."
Normal? Im not sure what is ever normal or not ... but, being obsessed is never a good thing...