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Based on your mention of Discovery Writing, maybe you are or you aren't; perhaps you haven't "discovered" it yet. It might be that what you're describing is some form of resurrection or "zombific...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/33688 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Based on your mention of Discovery Writing, maybe you are or you aren't; perhaps you haven't "discovered" it yet. It might be that what you're describing is some form of resurrection or "zombification curse". Your mention of curse reminds me of the Dark Souls series of video games, in which the player character and many NPCs are "undead" but have retained (at least some amount of) sanity. The player can and likely will die often. An undead's dying can lead to it becoming hollow, a state characterized by little or no sanity and decayed flesh. Depending on the game, this hollowing has different gameplay effects on the player. If you're definitely wanting to distance yourself from stereotypical zombie traits, you can figure this out yourself with research and playing with it. Ultimately, like other answers have stated, it is up to you; however, **since you're writing by the seat of your pants, you may not even know yet.** Perhaps your thoughts now are that your character may not be a "traditional zombie", but maybe you'll find something out later.