My significant other has EDS, diagnosed within the last couple of years by a rheumatologist. Since then, we've found some physical therapists are quick to dismiss us when they find out Ehlers-Danlos Syndrome is involved. There seems to be a rule that if they don't have experience with EDS, it's in their best interest to not try to help.
The upside is, doctors who know of EDS are suddenly much more invested in my SO's well-being on hearing they have it. The doctors end up doing what they can and recommending others in their circles who have experience with EDS.
From my view, it doesn't magically open doors, but it does help screen doctors for their ability to help out. Along those lines, if your doctor isn't willing to screen you for EDS with simple things like the Beighton scoring system, it gives you a good chance to find someone who is.
But overall, my opinion would be to not discount your ability to self-diagnose, especially if you have people in your life who are suspecting EDS may be involved. My SO and I see things in their daily life that a doctor would likely miss in our rushed appointments.
Best of luck with your appointment!