Tapeworm - Reinfection

Hello!

My 2 year old cat had (possibly, we're not sure because the vet didnt
know what he was doing and since we have changed the vet) roundworms
and tapeworms.

After the treatments, she was back to being a healthy cat, running
around. Her anus was bleeding a little, but after the treamtments she
was fine.

Now i noticed that under her tail are little yellow rice-like piecies,
which I know are tapeworm eggs (no bleeding). But she hasnt been
outside since she's gotten better. Which means we have fleas in the
house that we're unaware of? The vet never saw any fleas on her
person, and she doesnt scratch herself often.

How can we prevent reinfection?

Thanks! (we're taking her to the vet hopefully tonight.. not sure about
their holiday schedules.)