Tapeworms are contagious to Humans and other pets. Usually a tapeworm segment will appear outside on the dogs rear end. Usually stuck in the tail or fur or in their bed. When dried up, they look like a grain of rice. If you put them in water and hydrate them, they look quite different. Since you already have an established Vet, I'd give them a call to see what to do. You may be able to just take the stool sample in and save a Vet appointment price. The medicine for this is one pill, dosed by weight. I would'nt wait.....
I would make an appointment sooner. They will probably have you bring in a stool sample and prescribe you meds. You will want to take care of this asap. When my dog was a puppy he had roundworms and they are disgusting when they come out- not to mention health issues....