Copyright is not the same as Trademark. You must enforce trademarks, not copyrights. Copyright is much stronger than trademark.
If they've directly copied from your application, you have very solid grounds for a lawsuit. I would go see a lawyer. In a strong copyright case (e.g. where you can prove you wrote it), a lawyer will take the case for nothing. Or, even if you're paying out of pocket, you will win if you can prove you wrote it. And when you win your competitor will pay your court costs and damages.
You aren't going to make a killing, but your winnings will give you another month or two of runway, and will shut down a competitor that shouldn't be allowed to survive.
I'm anti-lawsuit on pretty much every count except for copyright infringement (and I have been involved in a copyright infringement case in the past; $30k settlement). It's just nasty business for someone to steal your labor like that and pass it off as their own.