Simple answer: No. You'll need some kind of outside source. That source could be as local as the router if you had access to it, but it's more work than it's worth. And if you're on a hosting solution that's out anyway.
I assume your reason for wanting to get this quickly is for speed optimization? If so then I recommend you not worry about it. It's such a small action it won't have any lasting impact.
Now that I think about it; you should already know your public IP! If it's a hosted solution it ought not to change so you can get it once and just hard-code it into your project. I have no experience with heroku though, so it's possible they use a dynamic IP.