I had nail fungus on toes and fingers.
A general practitioner I saw said that I shouldn't do anything because "many people" get the condition, "nothing really works," and I should just accept it.

Not likely.
Saw a foot-doctor. At my request she prescribed
Pen-Lac, because it seemed to have worked for me on a prior condition. She also said Listerine and other anti-plaque washes work: just swab the infected area. Keeping the nails cleaned and dry is supposed to help, but now I doubt it. I think the fungus is almost inescapable. Whether it comes from old, moldy books, wet floors, old socks, shoes, sweat, air, or whatever.
So I did both. I used Pen-Lac religiously, cleaned the nails with alcohol (
"hic!" 
). I was told I could clean them every day, or every few days; I don't know which works better; and ocassionally swabbed them with an anti-plaque.
The toe fungus is very nearly completely gone.
The finger problem, not.
It looks like you have black streaks in your nails, as do I. My toenails had no black streaks but were yellowish and brownish. So I must have two different kinds of nail fungus, or which I have been informed there are "four major categories." So Pen-Lac doesn't always work.
I have been cutting down my finger-nails, the discolored section, a little less than 1/4 the entire nail area, in hopes that exposing the skin

and then, if the problem is with the skin underlying the nail finding some way to treat it myself

, and if it isn't the skin, I'm hoping once the nail is removed far enough, when it grows back, the problem won't.