Ok I just read through and there's a ton of misinformation in this thread so I'll simplify it
Revolution is very safe and rats tolerate it well. If you check.the MSDS it takes a TON of it for LD50 in rats (much safer than ivermectin by far). Kitten/Puppy and Cat are all 60 mg/ml concentration, while Dog is the same formulation but stronger at 120 mg/ml so you would use half as much. You can dose Revo at 6-10 mg/kg.
I order my Revo online but you can check with friends, family or even your vet to see if they have any.
As a rescuer I usually dose ALL incoming rats as a preventative with no issues.
You express the tube into a small bottle with a tight lid/cap, pull up.your dose and part the fur on the back of the shoulders or neck, trying to get the med as much on the skin as possible. It absorbs quickly through the skin into the bloodstream this way. I usually dose and walk away, no e-collars or distraction. Remember to put your lid back on right away as the alcohol part will evaporate quickly and it will dry up.
Here's the article I made up to show the difference between mites and lice, although yours sounds like a case of mites from your description.
http://lilspazrathospice.blogspot.com/2016/11/whats-on-my-rat-ectoparasites.html?m=1