Hi Rebecca,
I guess everyone is going to have their own opinions on this.

I think Jilliebeanmn is right. Trust your gut...
But since you're asking... I would say personal means, well, personal. Life is messy and we can't always separate our personal and work lives. Often, when you share a bit of youself this way you will find others who can realte to your human-ness/ your struggles. Who knows... Your professor may relate to what you've written.
Supportive thoughts your way.
E