Wordpress on AWS EC2 - broken after assigning elastic IP

Question

So, I got WordPress installed and working just fine. I can access the site and the wp-admin via the public DNS that I get from the instance.

However, once I create an elastic IP and associate it with the instance, I can no longer access wp-admin and the home page style sheets and JavaScript files are not loaded.

I am attempting to access the site and the wp-admin using the new public IP from the elastic IP. The same thing is true if I try to use the public DNS from either the elastic IP or the EC2 instance.

When I view the page source I see that the reason things aren't loaded is that the URL for all of the assets (.css, .js. etc,) is pointing to the bold public DNS

When I disassociate the elastic IP things do not go back to working again.

I'm missing something but don't know what.

Any help would be appreciated!!