It looks as if you're offline which, hopefully, means that your vet called you back with suggestions.
Otherwise, I'd not induce vomiting since I'd worry that the chemicals might do more damage to her esophagus (if she drank a lot of the water, that is), especially if she's already coughing (which could mean that her throat is irritated).
If she only drank a small amount, then there's less of a concern for significant toxicity.
If this were my case, I'd suggest Pepcid AC (famotidine) as opposed to Pepto Bismol at a dose of 1/4th mg per pound of body weight twice a day for a few days.
I'd monitor for signs of balance issues or mental changes; should they develop, a vet visit will be prudent.
More than likely, the chemicals were diluted enough in the pool water such that she'll be fine...hopefully, this is the case, anyway. Deb