Wow, I haven't had that happen to me. But I will use shampoo once a week usually. I've also been using a boar bristle brush to distribute my natural oils. When I do wash my hair, I try to only wash my head, not all the hair down my back.
Is your hair long or short? If it's long, maybe the rinse didn't get all over your hair and there was still the residual ph imbalance from the baking soda. Not that that should make your hair fall out, but could explain why it feels like hay.
Female, 5'3", 49, Starting weight: 163lbs. Current weight: 135 (more or less).
Starting squat: 45lbs. Heaviest squat: 180 x 2. Heaviest Deadlift: 230 x 2