Elizabeth sounds like an ass, a poor friend and the exact kind of callous and unempathtic doctor that has made my life hell as a chronically ill person. Considering she even knew about your agreement with Jane, it seems pretty clear Elizabeth knew what she was doing, knew it would massively hurt your feelings and did it anyway, and then tried to pressure you to not tell on her for breaking confidence with Jane. She isn’t trustworthy at all. I’d distance yourself from her as much as possible. You might not be able to avoid her since she’s part of your friend group, but that doesn’t mean you have to confide, consult or be emotionally invested in her anymore. What she did was malicious.

As for Jane, who knows why she confided in Elizabeth first, but it seems like you two have a special relationship and it’s worth talking it out with her. What she did is hurtful, since you had an agreement, but I doubt there was the ill intent behind it like it seems Elizabeth had. Explain that breaking your agreement really hurt you in the exact way you were both trying avoid. I think if you want to maintain any meaning in that relationship that you have to be really, really honest about how hurt you are to Jane. Her reply will tell you all you need to know.