Simple chemical tests are prone to giving false positives, that's why we don't use them very often.
It's hard to say why without knowing the exact chemicals; for example if the alcohol was aromatic, like phenol, then that would react with bromine via electrophilic aromatic substitution. The carboxylic acid could react with bromine to give off HBr gas.
Or the bromine water wasn't the in the best condition to start with.