PvP as healer (paladin)

Playing the healer role in battlegrounds can be both very rewarding, and a somewhat frustrating experience, all depending on the situation. Battlegrounds are designed with teamwork in mind. This includes movement between objectives, and it means watching out for each other. While it is the healer's job to keep everyone alive from a technical point of view, it is everyone's job to keep the healers alive.

Strategically, Battlegrounds usually play out something along the lines of kill/CC healers, then kill the rest. If you find that you are a sole healer in the Battleground, you can expect to be one of the first to be targeted. It is partially your team's job to look out for you, and to "peel" players off of you, allowing you to do your healing job without being swarmed. Moving in groups is almost always recommended, and making sure that the group has some level of synergy helps the overall goal of staying alive.

When it comes to who you should heal, -- well, everyone that is close and being targeted. If you are playing Warsong Gulch it is probably reasonable to say that you should prioritize keeping the flag carrier alive if you are faced with the situation of having to pick a target to heal while letting the other die.

That being said, there are some things you can do as a healer to stay alive longer, such as use objects and geometry to hide your visibility, or attempting to keep your team mates between you and your opponents, effectively forming a "wall" of players that the opposing team has to move through before getting to you.

My suggestion to you would be to go out into the battlegrounds and try out different things. Figure out what works for you, and what doesn't, and then go with that.