I don't think it sounds like hairy tongue. I think it is candida albicans. Its basically a yeast infection of the mouth. If it persists after the antibiotics your doc will probably prescribe a rinse like nystatin, which is a swish and swallow medicine.
If hairy tongue developed after administration of antibiotics and chlohexdine mouthrinse,the tongue condition probably resume normal staus after discontinuation of antibiotics.