I cannot get CORS working

Let me preface this with the fact it’s my first time setting up anything in a cloud server, and my previous knowledge consists of doing a local WAMP stack and using web hosting solutions.

I’ve set up an Ubuntu LAMP Install fine, and what I can’t get to work is the CORS! I suspect the module headers, because I don’t seem to get any change on my response headers. I’ve enabled the mod:

sudo a2enmod headers
sudo service apache2 restart

I tried the same .htaccess I used before doing the migration, but it didn’t work, thus for testing purposes I’m using only:

Header set Access-Control-Allow-Origin "*"

Then I did a apachectl -t, which gives me Syntax OK. The following is an excerpt of an apachectl -M:

headers_module (shared)

It should be working, but it’s not. What am I doing wrong?