Pushing your way through 5-man dungeons, yelling at DPS to CC, making tanks run around avoiding circles, drinking after every pull, constantly wiping because you are OOM... it's worth it. Running your first heroic at 329 iLevel really will be barely past the minimum. You shouldn't expect it to be easy. You should expect to wipe, and many times at that. You should expect it to be difficult as it is the level that Blizzard considers to be the bare minimum to get you through. And if what I'm reading is accurate, you are making it through, kicking and screaming along the way. Yes you will go OOM not only because your tank isn't geared so isn't reducing damage, but also because your DPS is lower so bosses are taking longer.
As you gear up, not only yourself but your tank and your DPS, you will start to see these current "necessities" fade. Focus on gear that has Stam/Int/Spirit + Haste. These are must-musts. Haste is more optional as you can reforge for haste, but I'd say every piece you are wearing better have spirit on it. It is pretty crucial.
Where can you see yourself in the future? I'm not saying that I'm a paragon for the healing model as it stands, but I do strive towards it. I'm in many BiS pieces for pre-raiding gear. Currently I run with a group who are all ~340 iLevel and can tell you that a) I no longer drink between pulls and b) do not go OOM during a boss fight. [And let me tell you, I've had to face harsh criticism for why I was always going OOM, but those angry sentiments have long since faded, even lauded as I now can end fights with 50-75% mana]
But this doesn't mean this is all on my part. DPS has to watch for harmful circles. Tanks need to use their cooldowns when necessary. And trust me, at the end of every boss fight, I've used every single cooldown I have at my disposal. If I had a screenshot of my action bars, they'd all be 2-5m in delays.
It's a tough path but I really have to applaud Blizzard for making heroics be heroics. Wrath heroics in my opinion where way to easy. These dungeons reward you for learning the fights properly to gear yourselves. Once geared, they appropriately become easier to handle and heal. For those jumping off the healing ship, I feel bad for you because the road ahead is so much brighter yet you can only look at the darkness around you now.
Very pleased healer who's thoroughly enjoying new dungeon scene