First of all, DPM is not dose. Disintegrations Per Minute is a measure of radioactivity. 1900 DPM of Pu-238 would be 863 picocuries. Too many unanswered questions to come up with a reasonable estimate of dose from that limited information. Since that activity was measured on a nasal swab, that's not really representative of what was actually inhaled and got trapped in the mucus lining of the respiratory system. And since you can't reliably measure alpha-emitters with a whole-body counter, you would need to provide some bioassay samples (urine or fecal) to a qualified analytical laboratory. Then a qualified dosimetrist could use that information to make a dose estimate.
863 picocuries of Pu-238 is 123 ALI (stochastic Annual Limit on Intake) per 10CFR20 appendix B. That's not a huge amount, but it's not insignificant either. I wouldn't want to speculate what the actual quantity of material was breathed in. Only bioassay samples could tell you that. Another factor is what the material's particle size was, which would determine whether the material will eventually be transported out of the lungs in the mucus (larger particles) and swallowed and excreted (resulting in an ingestion dose which would be a smaller dose), or whether the particles were small enough to be retained in the deep parts of the lungs (resulting in a true inhalation dose which would be a larger dose). Another factor is the chemical form of the material, i.e. soluble or insoluble in tissue fluids. Soluble means it could be more easily absorbed and transported throughout the body.
From your limited information, it sounds like the intake was not large. I don't think there would be any short term effects from that amount. If the material was absorbed and transported throughout the body, it would accumulate and show effects at the bone surfaces. And it would most likely take quite a few years. The effects are called "stochastic" which means there is a probability associated, which means the effects may or may not be seen. The higher the stochastic dose, the higher the probability of seeing the effects.
There are a lot of gaps in my explanation. You need to talk face-to-face with a qualified internal dosimetrist about followup bioassays and long-term effects. The licensee where you work is responsible for providing you all the information you request about this. Keep asking questions until you get the answers. The folks at REACTS in Oak Ridge could also answer your questions. Good luck.
