We have in Sotah ~42 that if a person has too much zevel coming out, he needs to check the status of his health and fix himself before things became worse. Similarly, B Metztya 107 talks about people being responsible for effects of cold and heat and how a healthy breakfast (bread, salt, water) has so many physical and spiritual benefits. At the same time, Sotah also says that Hashem protection is limited to people who do not have aveiros…
So, you need to read BB 116 in the context of these other sources. My suggestion is that one first checks his health, then checks his aveiros, and only then go to the chochom (not simply a talmid of one). Just for the simple reason that we, R’L, have more sick people than Chachomim, so the latter need some time to learn. Do you have a better explanation that covers all sources, not just one?
R Elchonon’s statement seem to contradict all of the sources, whether requiring refuah or going to the chochom. also, requires an explanation.