Is there an app that will forward my texts to another phone?

Yes, but depends on what phones you're using.

Just google the exact title of your thread and you'll get some hits. Android I think is pretty damn simple

Try pushbullet. It allows you to access your messages from another device but it has to be on for it to work.

Put the app on both phones and you work phone will ding when the personal phone gets a message. It works both ways. Can also install on your pc to send and receive messages.

It has limitations but it's the best I've found bc I don't like carrying both phones all the time.