For Brayflox, there is an entire set of level 32 green gear (ilevel 34) that can be won from it. I kept all the gear I won the first time through on WHM and reused it for SCH. You should probably have level 29 right-hand-side gear as well (those you get from Haukke)
Though you don't necessarily need all of that if you were able to get to the final boss. The problem with the final boss is the tank not pulling the boss out of the poison fast enough.
Now, just for reference, the difference between doing this on WHM and doing it on SCH mainly comes down to WHM "Use Esuna", SCH "Heal through poison stacks", if you get paired with Melee's, the latter only lets you heal the tank, so the Melees need to avoid stepping in the poison completely. If you get paired with ranged DPS, then there is no reason for them to take any damage (though they inevitably will, you may be able to ignore some of it.)
So it sounds to me that maybe the overall party was just barely meeting the DPS requirements. You should have put your bonus points into Mind and nothing else, but if you put it into PIE, then you should have still not run out of MP.
Generally you can, and are supposed to play harder content without collecting the entire set of gear from a dungeon because you aren't guaranteed the drop you need. That's when you make up for weak gear by buying it off the market.
As for strategy... You are a healer. You should be using Cure I unless a large amount of HP needs to be cured at once. It's sometimes more effective to use Cure I 4 times than it is to use Medica (but it will depend how spread out the party is.) You won't have Regen until level 35, and generally you don't want to "proactively" use Regen or Medica II due to the enmity costs. Don't feel pressured to DPS, that's the first mistake everyone makes, the amount of damage the healer contributes will likely never be more than 8%, so it's not enough to justify taking attention away from healing. You get Shroud of saints at level 38 and Divine seal at Level 40, which let you temporarily change the dynamics of the healing. Shroud of Saints has an effect called "Refresh" which recovers MP for 15 seconds. When you initially get it, you probably won't notice it (and I don't believe anything in the game actually says "recovers MP" but it's nowhere near as handy as how MP is generated on THM/BLM and ACN/SMN/SCH.) Divine Seal boosts your healing by 30%, so when you're "near low", like the bottom third of your MP you can hit both and economize Cure I's. My preference however is to use Divine Seal before Medica II to boost the power of the regen effect.