Originally Posted by
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You don't deal with them.
Even if you did, you'd just spam heals so hard no double DPS team could ever beat you.
PvP, right now, is broken and practically unplayable. If you're not CC locking a healer, they're never going to die. Blizzard, apparently, thought the best way to deal with how broken Healers were was to just make CC rampant and uncontrollable.
What you can do, aside from rerolling Resto Druid, is just have your partner learn to snap-target onto a warlock or mage when you see them casting something, and then interrupt them. As a Paladin, unless I'm mistaken, you don't have any interrupts (do Holy Paladins even get rebuke?), so you're going to be totally dependent on your arena partner to interrupt stuff.
Also, try to fight around pillars. If you're getting casted at, quickly throw a big heal on your partner and then LoS the cast quick.
For as bad as PvP has gotten, there's still a few tools you have left to deal with things, but don't feel bad. It's really not you or your performance as much as it is just PvP being deplorable.