I think the friend meant to be encouraging ....
I'm afraid I don't see anything encouraging in "you're not really sick, and your doctor is wrong. Put on your big girl pants and deal." The friend meant, in my opinion, to let the OP know how much more knowledgable she was about everything, more so than the medical profession and the person having the symptoms.
If someone posted "my doctor told me I have 1 week to live," replying "maybe they're wrong" is trying to be encouraging. To respond to "my doctor finally gave me a diagnosis, and the treatment is helping a lot," with "Nah, you're not sick in the first place, your doctor is wrong about it," is condescending. In fact, it's quite dangerous, because it could lead to a suggestible person abandoning appropriate treatment.
I don't think that we know that was the tone of the OP's post, do we? To me, it makes a difference. If someone posted about being diagnosed with something and sounded upset, I can see where Friend's post could be taken to be encouraging. There really ARE a lot of "new" conditions out there that would have been considered in the range of normal 20 years ago.. putting a label on it can be scary to some. I'm thinking of a certain condition that a friend of mine has said I should be tested for.. one primary symptom is fatigue. This was suggested after a day of walking, when I was really tired. Well, no, I'm tired because I'm overworked, overweight, and don't sleep right or get enough exercise, and we've been walking around all day.
I'm going to go against the grain here and say I think while friend may have overstepped a bit, I would have given her the benefit of the doubt and assumed she was trying to be helpful. I think that OP's reply to the FB post was unnecessarily harsh, and really an over the top reaction. I can see why Friend responded the way that she did, I would have been pretty offended to have received the email OP sent. I think maybe a "Thanks for your concern, but my doctors have done the tests and I'm happy to finally have a diagnosis." would have gotten the message across much more politely.
I think if you want to mend the relationship
, I'd apologize for being so harsh, and maybe blame it on the emotions of the diagnosis. I think it'd be okay to say that you may be a bit touchy about the diagnosis because you know that some view it as false or self-inflicted, so that colored your view of what she wrote. But only if you want to.