From the first to chapters the main character doesn't feel like a zombie. The main character still apparently does everything normally except having a heart beat and healing faster than normal. She still has a personality and feelings. She still breathes (breathing in needed for talking). She still sleeps and probably still eats and has other bodily functions. If anything else was different the author would have pointed it out already (or will very soon). So she might be undead but so far its just conjecture that she is a zombie on her and her friends part. A walking talking corpse she could possibly be but a zombie she is not.