I think part of it is that your timing as a SCH is a little off.

WHM and SCH function differently:

WHM is a reactive healer. Damage happens, you heal it.
SCH is a proactive healer. Damage is about to happen, you toss shields.

You need to know the fights well enough to realize there's a big attack coming and to put shields up before it hits. It does no good to shield after the fact. Even trying for the shield while the boss is casting can be too late if it's faster than you are... unless you {Swiftcast} it.

In the AoE case, this is how it plays out for WHM:

Boss health hits 51%.
Boss health hits 50%.
Boss does AoE attack.
Health bars drop.
WHM -> {Medica}

For a SCH, though, the optimal order is different:

Boss health hits 51%.
SCH -> {Adloquium}
Boss health hits 50%.
Boss does AoE attack.
Shields absorbs damage from attack.

You should set a focus on the boss so you can watch the cast bar.