What operating system is your server running? I can't comment yet, so I had to ask, here. Yell at me if you must.
From my understanding Route 53 can do a few different things, but to your point, you manage your certificates through GoDaddy.com, so I don't believe you will need to use AWS's Route 53 service for this. You will need to however make sure that your url resolves to the AWS EC2 IP through GoDaddy.com. I've found that certbot simplifies the process quite a bit and there is a guide on digital ocean for CentOS (pretty much the free version of RHEL) here:
https://www.digitalocean.com/community/tutorials/how-to-secure-apache-with-let-s-encrypt-on-centos-7
The basic steps are:
Install epel then the required repos (you may already have httpd and mod_ssl installed I presume):
sudo yum install epel-release
sudo yum install httpd mod_ssl python-certbot-apache
Make sure your firewall rules are in order and allow for https, usually 443 or 8443 depending on your setup...
Now run certboot and replace example.com with your urls
sudo certbot --apache -d example.com -d www.example.com
You will get some prompts to answer. If your virtual hosts file doesn't specify your domain then you will be asked to choose a file, ssl.conf should work fine. Choose HTTPS (and HTTP to HTTPS redirect if you desire). Your certs will be installed at /etc/letsencrypt/live
Thats really it, certbot should have done some checks and make sure you're in control of the domain name and modified your apache configuration to use the certs it installed. There are some other security hardening techniques that link goes through but that is out of the scope of the question.
This of course assumes you're not using a load balancer in AWS, If that is the case, then you will need to install your certificate into the HTTPS listener on the load balancer. More here: https://docs.aws.amazon.com/elasticloadbalancing/latest/classic/ssl-server-cert.html
Hopefully that helps.