As far as I know, IVIg is not given to patients with ME/CFS and no other indications in any reputable treatment centres because there is not enough evidence to support it.
One, the risks of giving it outweigh the potential benefits (which until there is sufficient evidence have to be considered as none)
And two, there’s a limited supply, so even if the risks were negligible, it’s not something doctors can just give a try, because they would be taking away from the supply to patients for whom it is proven to be life saving.
But there do seem to have been some reasonably promising trials some years ago.
I was very surprised to find this one in Australia of 49 people (!) in 1990.
https://pubmed.ncbi.nlm.nih.gov/2146875/
However, it says that 40 of the participants had “abnormal cell-mediated immunity”, so I guess that counts as an indication, at least in a research setting. I wonder what happened to those people down the road.
(I looked into IVIg a bit after a specialist made an offhand comment to me that “you could try to qualify for it”. Turns out there is absolutely no way I would qualify for it here in Australia with my current illness, even if my symptoms got a lot worse. Confirmed my opinion that that specialist was a twit. Imagine if I had taken his words at face value and started pursuing an unachievable treatment, plus the disappointment when I didn’t get it after perhaps a two-year wait to find that out.)
I’m sorry you can’t get testing for SFN.