I volunteer weekly, and I've never had to have a doctor sign anything to say that I'm a healthy person able to work. I'm wondering if that might be specifically related to the kind of activity, especially if it was an overnight camp. I do think there might be other organizations you can volunteer with to build your resume that don't require such a letter. In my experience, most do require police checks, especially if you're going to be around children, but the police checks should only record convictions. You may want to explore other volunteering opportunities.
I'm in Ontario, and psychiatry here is like everywhere else - good with a good psychiatrist, bad with a bad one, outdated with a psychiatrist who's out of date. Every single one of the psychiatrists I can access for free are foreign-born. That's simply the way it is right now - most Canadian psychiatrists leave Canada or go into private practice, people from foreign countries are incentivized to come to Canada to practice, and it's probably even worse in the country they're originally from. But still - a psychiatric appointment may be useful in providing you with a diagnosis. You wouldn't need to see a psychiatrist regularly, and given that they largely exist to diagnose and dispense medication, it would make sense that they spend lots of time on schizophrenic and bipolar clients who tend to be on medications to treat their conditions. You don't want to utilize medications, so you wouldn't need to regularly see a psychiatrist for medication checks. I know it's not ideal, but few things in life are.
During your intake appointment, you can specifically request someone who speaks English fluently, who has lived in Quebec/has some knowledge of your culture, etc. You may not get what you ask for, but you may also be pleasantly surprised by what you do receive. But again - until you have actually accessed the care, you don't know for sure whether they can help. Even if/though you've accessed (or tried to access) care before. It's not a static system - new people, new ideas and new policies are introduced and the care that's provided can, and does, change.
Support groups exist because they can, and often do, function therapeutically (in the sense of having healing powers). I attended a group for stress and anxiety where the bulk of the members there had PTSD. In some ways, that group did more for me than therapy ever did, because suddenly it wasn't just my experience (or failure or fault) but a rational, sane response to some really awful things. It was elucidating to me in a way that therapy couldn't be. But had I simply dismissed this group in advance, without even making a good faith effort to try it, I wouldn't have known that.
You wrote that the original event happened several months ago, and also twice that the symptoms are getting better. How many months ago did the event happen? If the event happened within the last X months and the symptoms are getting better on their own, without treatment, then I think it's classified as an adjustment disorder rather than PTSD. I'm not sure if that's changed with the new DSM and perhaps I'm remembering incorrectly, but I do believe that was something I came across many times in my early days of research. I'm not attempting to minimize your situation, but I am presenting a possibility to you.
Another thing I'd like to suggest to you is that you seem to have a particular investment in believing that all of the avenues for health care are inadequate for the currently undiagnosed mental health issues you have. How can you know that in advance? Yes, it's hard, yes, it's imperfect, yes you will have to advocate for yourself - but that's what we all have to do if we want to get better. We have to do what we can with what we have - and while you may feel like what you have isn't good enough, I maintain that you don't know that yet *and* that I honestly find it hard to fathom someone who is complaining about their imperfect access to free health care on a board with so many people who have no money and no access whatsoever to any kind of health care at all. I'm not guaranteeing that you will get the care that you need and deserve (but I hope like hell you do), but I am saying that it rubs me the wrong way to have you scoff at the services that you haven't availed yourself of yet for this particular issue. How are these beliefs and approaches benefiting you? Are they benefiting you? It is a very hard thing to need and ask for help, but how are you any better off *not* asking for help you need? If you don't actually need the help, then would you be here and why? If you do, why not reach for it?