I was diagnosed with chronic Lyme. I'm not attached to the diagnosis, and it's something of a catch all and more investigation is needed to get real clarity on root issues. There are a handful of issues that tend to cluster together -- chronic infections like Lyme, heavy metal toxicity, exposure to toxic environmental mold, severe nutrient depletion, to name a few. Seems a lot of suffering can come from dysregulation in the endocrine system especially HPA axis and thyroid.
Leaky gut, yep this could also be a key problem. When the gut lining is damaged by antibiotics, NSAIDs, processed food, pesticides, etc you're looking at potential systemic collapse. Its our primary defense against the outside world. It's where many neurotransmitters are synthesized. Sick gut = sick brain.
The mainstream medical system is not set up to deal with these complex, chronic illnesses. My advice is stay away. I have heard many stories of terrible treatment from ignorant and arrogant MDs in cases like this. Typically the best you will get is some sort of synthetic drug cocktail that will knock down symptoms, while various disease processes continue unabated. Good chance you will also get a lot of "it's all in your head" responses. Lyme is also controversial and politically charged. Many mainstream MDs will deny its existence and will get quite hostile.
As for psychiatrists, i can't think of a worse option.
Naturopaths and Functional Medicine MDs are good place to start. Practitioners of chinese medicine are also worth trying.
Lyme disease is known to cause chronic inflammation of the brain and nervous system, which can lead to pretty severe psychiatric symptoms. Mercury toxicity also can cause terrible brain symptoms. I used to have stable mood, reasonably robust mental health, and excellent physical health. Now i am a mess on all levels.
Not saying your sister does not have psych problems that are independent of these physiological conditions, but when you have a large constellation of symptoms, then i think treatment needs to be holistic and comprehensive. Not sure about the germaphobe stuff. That is a bit concerning. Maybe an OCD type thing? If it's new, I'd wonder what has changed in her brain.
Is it possible the research she is doing is legit and she is refusing the treatments offered based on sound reasoning?
I also suggest finding a biological dentist to evaluate oral health.