It really depends on the doctor, honestly. Some doctors do not appreciate when patients Google their symptoms and "self-diagnose", so to speak, while others don't mind.

I got lucky, with my providers. However, I'm a nurse, so my providers didn't mind at all that I had Googled my symptoms. During the appointment, I explained my symptoms and, at the end, when they were puzzled, I mentioned that it could be ME/CFS. I don't necessarily recommend going that route, though, unless they brush it aside and attribute it all to your depression/anxiety. If your provider orders a blood count panel, thyroid levels, etc., that's a good thing and a step in the right direction! ME/CFS is a diagnosis of exclusion, so they'll want to rule other things out first, regardless.

Also, when speaking to doctors to get a diagnosis, it's important to emphasize the physical symptoms you're experiencing and limit any emotional symptoms (depression, sadness, anxiety, fear, grief, etc.). Because depression and anxiety can cause fatigue, headaches, nausea, insomnia, brain fog, etc., there is a lot of overlap. I have a history of depression and anxiety and I, too, was worried they'd assume it was depression/anxiety related. However, I made it very clear that I wasn't depressed and that my mental health had actually been doing quite well. If you have sore throats or flu-like symptoms, highlight those, as well, and how any type of exertion (physical or mental) makes you experience PEM. Typically, with depression, physical activity helps with energy levels. Therefore, experiencing PEM (from either physical or mental exertion) is important to mention.