A couple observations first.
Unless Jesus was healing crowds, he addressed the sin issue along side the healing. I find this significant given what James says about the anointing of oil for the sick. Seems to me there is a lesson here.
Modern medicine has deteriorated to a business with profit in mind, never mind the victim. It is all about money. I have four family members active in the medical profession - one sister, two brothers-in-law, one daughter-in-law. Some lament much about the greed that drives the medical profession, and the pharmeceutical companies.
Ok, now about praying for the sick. The following is my own testimony - not given as the formula but how God has worked in my life.
God has shown me by experience that many ailments are rooted in spiritual distresses. Or, call it emotional stress. When I cast all my emotional, spiritual baggage on him, leaving it at the cross, healing will occur. The physical symptoms of this stress included bursitis, asthma, sinusitis, carpel tunnel syndrome.
As life trots on, when we find our selves ill we pray for recovery. A few years ago I had such severe pain in my hips that I called for the anointing of oil by our pastors. I was not healed instantly but I never again experienced the pain I did that one night. Later I did feel led to take a nutritiional supplement MSM. Today I am no longer a candidate for a hip replacement which is what the doc told me I needed. Some pain still exists but it is not debilitating, and I have learned to respect my body - that it is no longer a 45 YO but is ageing and I need to respect that it is wearing out and to treat it as such.
We pray a lot, me asking my husband to pray for me and the LORD heals. I may have experienced an instantanous healing - not sure but I give God the credit for my recovery. (I was dreadfully sick last fall. I hurt everywhere, I mean everwhere a body can hurt I did. I came within a whisker of asking my husband to take me to the ER when I decided to ask him to pray for me instead. He did, and I fell asleep, slept hard for several hours. When I awoke I felt perfectly fine - so good I felt like getting to work! But chose not to, giving my body a rest and besides it was the LORD's Day - a day we refrain from unnecessary work.)
At the moment my 70YO husband and I (67YO) are not on any meds whatsoever. We do not get physical check-ups either, much to the consternation of some folks. "If it ain't broke don't fix it." I am of the mindset that if God wants me alive, it is his responsibility to keep me healthy and my job is to walk with him so he can. Once my job here is done and he wants to take me home, I will not fight that by imposing upon others huge medical bills by pursuing expensive medical treatment.
Seems to me the issue is not so much healing but whether we are ready to meet our Maker. If we are I suspect it will impact our dependence upon the medical profession and the pharm companies.
My opinion and testimony for whatever it is worth. I will not fault those whose opinions differ from mine on this issue.