Ask a new question, definitely. When the question changes substantially, it's cleaner and preferred to make a new question.
The existing question is done and editing it now would create a bit of a mess, what with an answer already being accepted and answering a different question. Further, the question is a decent one by itself, so although it might not be the one you meant to ask, it's a good question and doesn't deserve deletion.
For the new question, note that of the two example titles you floated, one is much better than the other. "How can we make up for a Warforged's lack of healing?" describes your actual problem: the Warforged's lack of healing.
Meanwhile, "What are all the ways to heal a living construct?" is pretty general, and there's no guarantee that it will even solve your problem as it's likely to get answers along the lines of "well construct X can be healed by X1, construct Y can be healed by Y1 and Y2..." with perhaps none of them mentioning Warforged! You could end up in the same place again, with good answers to a solid question, but nothing that actually helps your actual situation.
So if you post a new question, it should be along the lines of "How can we make up for a Warforged's lack of healing?" That's a good title to start from to write a nicely focused question that will solve the problem you're actually facing.
