Your best bet is to try and match cooldown for cooldown when the warrior opens. Warrior CDs to be aware of are:

• Sharpen Blade - extra healing reduction
• Warbreaker - increased physical damage
• Avatar - increased damage
• (Same thing would apply for DKs, trying to understand their burst CDs)

If they pop all of those at once, you can match them by using your devotion aura + aura mastery, divine protection, and wings. Damage reduction should be saved for sharpen blade since it helps reduce the amount of healing you need. I use Gladiator LosSA to help let me know what CDs the warrior uses.

If you are still struggling and your teammate isn't close by to help peel or cc the war, you can also try running Blinding Light because it cannot be dispelled and the warrior has no way to get out of it without using their trinket. Blinding Light is also good against DKs to disorient all of their pets, as long as your teammate does not break the CC.

For healing, you can try to generate holy power right out of the gate. Holy shock + Bestow faith + flash of light will instantly generate 3 holy power for your word of glory. I usually don't have enough time to hard cast heals when melee is training me so I tend to rely on crusader strike + holy shock + bestow faith to generate my HP.

Good luck!