You sound definitely hypermobile to me... I have just been through a (long) process of getting diagnosed with hypermobility syndrome. Here are a few insights I gained along the way...
There's a difference between 'hypermobility' and 'hypermobility syndrome'. Lots of people are hyper-mobile and have no problems with it. People with HMS, on the other hand, have or develop other problems - notably joint pain. The NHS use the Brighton Criteria to distinguish HMS from general bendiness.
I spent over a year trying to work out what was wrong, then waited 3 months to see a rheumatologist... Who confirmed the diagnosis, said basically there is no treatment other than exercise, and discharged me. You already have a rheumatologist, so I'd talk to her about your suspicions and (probably) get a confirmed diagnosis, but don't get your hopes up that the diagnosis will actually make much difference.
On the other hand, having a diagnosis could affect the way you live your life and your self-management. I'm almost 50, and if I'd had a diagnosis a couple of decades ago, I could perhaps have avoided some of the early arthritis that now affects me so badly, by changing the type of exercise I did, managing my weight better, wearing arch supports i avoided for so long, wearing better shoes, and - importantly - recognising I had a genuine problem and wasn't just moaning and pathetic!
HMS has all sorts of associated conditions relating to the fact that your soft tissues are generally lax, including low blood pressure, varicose veins, hernia... And depression which is hardly bloody surprising given the rest of it! For me, it explains a lot of other problems I've had, and stops me feeling like a hyperchondriac. :(
Also, HMS (but not simple hypermobility) is associated with some serious health conditions including faulty heart valves, so a diagnonsis means you and doctors can watch out for these.
And importantly, HMS is a genetic condition, so you can watch out for your kids too. My eldest shows signs of it... I now want him to get a diagnosis, so he can self-manage better than I did.
Good luck with it. :)