Shower head washer woes
As long as the shower head inside diameter is a standard size (which I imagine it is), you really should be able to find a washer with a built-in screen at your local hardware store (although I haven't tried myself so I could be wrong).

And still if you can't find one then you can just go with a standard washer without the screen.  (And maybe you could remove the screen from the broken washer and place it underneath the new standard washer that you just inserted.)

I think the screen in a shower head is not so much for aeration as to prevent contaminants from getting into the shower and interfering with the various spray patterns.