What do you suggest if my mother is coughing constantly her esr count is 100 but all other parameters are normal what's the problem?

Reflux: one possibility is reflux disease especially if the cough is at nighttime, dry and is aggravated by acidic food, spicy food, too much food etc

Lots of ideas: Labs are seldom helpful in explaining chronic cough. This can be due to anything from reflux to cancer to late-onset cystic fibrosis to a viral or mycoplasmal infection hanging on to old airway damage from inhaling noxious fumes (there are hundreds of cases after 9/11). She needs a good workup. The sed rate really doesn't tell us anything.