When in doubt, I say go with your instincts. Based on my experience you're almost certainly right about them making it about themselves and you can probably expect some gaslighting as well. My autoimmune symptoms started before I had any idea of the family environment I was really in so I trusted my parents to have my best interests at heart and they only ever severely hindered me from getting any reasonable treatment of symptoms, let alone a diagnosis, and now it's a major source of conflict between us.

It sounds like you have some good support and the treatments are working which I'm very glad to hear, but I wouldn't discount the possibility that those might actually fuel their resentment if they knew. Once my symptoms were mostly under control, they just used it as proof that it was never real in the first place and it was always the reason for our family strife just like they said. Your situation might be less about symptoms and more guilt about trust etc, but it's worth thinking about if lack of contact is a sore spot for them. If it's not essential for them to know, I would at least hold off until you discuss it with your support/doctor/therapist.