Cancelled is not the same as rejected. Normally applications are cancelled as there is something wrong with the primary data such as name or passport details
Sounds like they did their job correctly. Visa exempt is issued for tourism not for living in Thailand with your girlfriend. You need to find a proper visa that you can apply for that allows you to spend extended periods of time in Thailand. You don't look over 50 and your not married so your main options are the DTV or the Thai Privilege visa, other than that get a job or sign up for a course of study (which you'll need to actually attend and learn)
You don't have to get the DTV from your home country so you could consider coming to Thailand using a visa exempt entry to get a consultation and treatment plan at the hospital you want to use then travelling to a nearby country to apply for the DTV
The first thing to note is you can't get a DTV visa inside Thailand. You need to apply at a Thai consulate and there aren't any in Thailand so be very wary