Nuclear radiation cannot be detected by routine blood tests.
If you have inhaled radioactive material, you need a specialized whole body counter (WBC) to detect it. There are manufacturers in China who specialize in these types of nuclear instruments, you can ask them.
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Nanjing Nuclear Safety and Energy has developed a series of whole body counters for medical use together with well-known domestic universities and foreign core suppliers. When there is a need to focus on checking the radionuclide content in special parts of the human body, a longer period of measurement is required in order to obtain a relatively low lower limit of detection, for this reason Nuclear Security Nuclear Energy has designed the chair-type organ counter WBC-MedNaI.This kind of equipment can detect the nuclear radiation in the human body.
I hope it is useful to you.