My dogs actually reacted badly to probiotics, so your mileage may vary. Friends who swear by it were glad to have the gigantic tub I had invested in, though!
If it was a kennel-- id suggest finding a new one (and making sure all the dogs there are up-to-date on their bordetellas, etc)
The bordetella vaccine is virtually useless in a boarding situation. It's a live vaccine and actually GIVES the dogs kennel cough , and enables them to shed the virus to dogs who haven't gotten the vaccine, so that they get kennel cough, too. (In my experience dogs are sick within 24-48 hrs of getting the vaccine, and pass it on to other dogs in the house within days.) It also takes a couple of weeks to work, but boarding kennels don't care about whether it works or not -- they just want to cover their butts for any potential lawsuits, by saying "all dogs are required to have bordetella and we make sure they do!"
So what happens is that people call up and want to board their dogs, they learn they need the Bordetella shot, and they go get it and drop off their dog within the week. So during the dog's stay, the dog is shedding virus and sharing it with the other dogs, including ones who had had their vaccine months ago.
It's a cold -- if you treat the symptoms generally it resolves quickly. If it progresses into other things, obviously veterinary care is indicated. But in my opinion that's a canine vaccine that's causing far more problems than it solves. The very best kennels don't require it for that reason -- they don't WANT people bringing dogs into the kennels shedding the virus.
But the OP's problem is probably Giardia or some such thing, anyway, which is more a cleanliness issue of the facility than a dog to dog issue.