EC2 in public subnet reachable by public IP but not by public DNS

Your VPC automatically has a private Route 53 zone to which the private IP address of the EC2 instance is added. But that won't help you connect to the public IP address of the instance. You will need to have a Route 53 public hosted zone (or a public hosted zone from another DNS provider) and add the public IP address of the EC2 instance to that zone.

That you can connect using the IP address is good - it means that everything there is correct; it's a matter now of ensuring that the DNS records are in place.

Edit (based on excellent feedback from a colleague): I had missed that you'd mentioned the Public DNS that is automatically assigned. It is of the format ec2-xx-xx-xx-xx.region-name.compute.amazonaws.com which means you should be able to use that as well as the IP. My answer above applies if you want a custom DNS name.

Hi I also encountered the same problem. How did you solve it in the end