Healbot and Forcefield are extremely powerful, and I always recommend an engineer to new players if they're having trouble surviving. However, my melee warlock does using Manafield and potions for health regen (Soulseeker wasn't cutting it for me), Fireshield and Manashield, as well as Fractured Reality and Voidwalker for enhanced mobility.
A melee warlock using Burning Blade to generate Hellfire really needs + cast speed. I used chaos ember gems and item drops that had + cast speed as she was leveling. Once she started getting some of the Tier II bonuses, things got much better for her. But as you've experienced, the build is a slow starter, and it was painful for me in the lower levels as well. But once she hit her stride, ah, what a fun class to play
Miothan's proc warlock build does more damage, but the melee Hellfire warlock does quite well , and is better suited to my playstyle. My warlock has killed all the DF bosses in Elite w/o dying, although it usually took more than one attempt -- the Executioner was brutal for me! This was before fractured reality, so I'm pretty pleased how she has done so far.
You'll find generating Hellfire is not a problem once you get higher in level. My warlock can get the max 50 within seconds, which is desirable to maintain to boost damage.