unless she is on dry food only and an indoor cat, I would not be too stressed about her not drinking as they can be very sneaky about that (basins, outside drains etc). The coughing may simply be because the tablet got caught then moved on, but irritated the throat on the way down (I have had pizza crust do that to me). Unless she appears to be distressed by the coughing, I would give it ia bit longer before panicking ...