AWS and Exim4 - 550 relay not permitted

I am not very good with mail server configuration but I have an aws instance that can send mail to some domains such as mydomain.com. However, when I send to googlemail.com I get the error in the mail.log file:

H=(blerg) [95.144.47.184] F=<me@mydomain.com> rejected RCPT <user@googlemail.com>: relay not permitted

I have added the following into the DNS through Route53 but I am not sure that it quite what the error is referring to:

mydomain.com. SPF "v=spf1 ip4:54.229.217.48"

Does anyone have any pointers? I haven't managed to find out much that is helpful but I have played with Exim4's:

dc_relay_nets

and dpkg-reconfigure exim4 'domains to relay mail for' 'IP addresses to relay mail for' but with no success.

There were two possible solutions here:

1. Set the dc_relay_domains to * in update-exim4.conf.conf;
2. Use SMTP authentication to ensure that the sender is allowed to have unrestricted access to the sending capabilities of Exim4.

Going with option 2 is the only way to prevent an open relay and so I did that. I set an SMTP username and password in my mail clients (Outlook 2007, Thunderbird etc.) and uncommented the cram_md5_server and login_server authenticator in Exims /etc/exim4/conf.d/auth/30_exim4-config_examples file. Then updated with dpkg-reconfigure exim4-config.