In "Tasty Armageddon," Scotty notes that having screens up precludes full phaser use but does not stop photon torpedoes. Now, one can argue that screens are not shields, but usage in this episode suggests the terms are interchangeable. Does this ever come up again? I note that, sadly, Star Fleet Battles doesn't take this technical tidbit into account.
Whatever the writer intended with that bit of technotalk, in face of current accumulated evidence it's probably best to think that Scotty meant "if the shields drain all our power, we can't fully fire back with weapons that require constant power feed themselves (phasers), but we can fire back with weapons that we have already charged (torps)". That is, one can fire phasers through one's own shields at all power settings just fine. But one can't use high phaser settings if the shields drain all the juice. And they don't normally represent such a drain - but they can be "rigged" to do so (Scotty's own words) when a powerful and sustained attack is anticipated and evasion is out of the question. Timo Saloniemi
This happens again in "The Return of the Archons" where the continuous attack this time is much more powerful and ties up all the ship's power just to keep the shields up preventing escape. In "A Taste of Armageddon" the continuous planetary fire is powerful enough to tie up a large portion of the ship's power to keep the shields up to which doesn't leave enough for full phasers. It doesn't mean that the shields are blocking the use of phasers. If this were SFB, think of your Fed CA being attacked every turn where you have to throw all but 3 or 4 points into reinforcing the shields. You'd have only enough to power your impulse engine, life support and maybe half your phasers every turn... Although in SFB, I'd change the rules so that the photons are cheaper to arm and use