Thanks for contacting us with your question.
Tapeworm infestation is very common in our pets in Florida because of the large number of fleas here. As you note, pets are infected with tapeworms when they ingest a flea.
I would advise submitting a fecal sample for evaluation, ideally with one of the segments that you have noted. Positive identification will ensure successful treatment, and a fecal floatation test will identify any other intestinal parasites that might be present. Once the parasites have been identified appropriate treatment can be dispensed.
Flea control is just as important as deworming medication because if fleas are still present reinfection with tapeworms will occur. We have found that products containing spinosad (such as Comfortis or Trifexis)have been very effective for our canine patients.