Drugs containing radioactive substances remain in the patient's body after a nuclear medicine scan. Data shows that the exposure dose to family members living with the patient is only a few micro sieverts 24 hours after a scintigraphy scan and the exposure dose rate measured immediately prior to an FDG-PET scan is about 20 to 30 micro sieverts per hour (source: Reasonable and Unreasonable Medical Radiation Protection, Innervision ; written in Japanese). Since normally about one hour elapses after a nuclear medicine scan before another examination starts, the actual exposure values are probably even lower. Since most of the radioactive drugs are excreted via the urinary system, performing examinations after excretion reduces the exposure dose.
In the interest of the patient, sometimes examinations can only be scheduled after a nuclear medicine scan is finished. If you remain worried about radiation, learn about radiation by participating in training intended for medical radiation workers. Another idea is to measure the exposure dose using a real time dosimeter borrowed from the hospital and then evaluate the results together with radiation safety management personnel. If the entire hospital cooperates in finding a solution, the best possible solution should reveal itself.