Firstly, you do not need to use Route53 as your DNS provider - any DNS provider will do - you can even host you own DNS servers (although, good practise is to have at least 2 redundant servers hosting DNS).
Your registrar needs to be made aware of the name servers you are using (which you appear to have done). On these name servers, you need to point the domain in question to your elastic IP address.
For your domain name, you will use an A record to point it to your elastic IP
For any subdomains, you will likely use CNAMEs to point to your domain name (although, in some cases, A records may be appropriate).
DNS records (A records, CNAMEs, etc) need to be added on your DNS server (in this case, Route53) - if you are using the AWS console, there should be an option to create a record set - select an A record (ipv4) and you should be able to leave the 'name' as the default (just your domain name, without a subdomain).
dig of your domain, suggests that there is an A record setup for the www subdomain, but that there is no A record for the top level domain. So, when a lookup is performed for the www subdomain, the nameservers return the correct IP address, and you can connect to the EC2 instance. When you lookup your main domain though, no IP address is returned, and no connection is established to the EC2 instance.
It looks like you have it figured out - at the moment, your domain is loading (second level domain), but not your www subdomain, and a
dig shows that you now have an A record for your domain, but none for your subdomain.