Calcium sulphite shower filter: making things better or worse?

Hi there,

I am using the Sprite shower filter which has KDF and Chlorgon, no carbon.

KDF, as I understand it, is irrelevant to radioactivity concerns.

Chlorgon appears to be balls of calcium suphite (sulfite), commonly used as the active ingredient in dosimeters, if I am understanding it correctly.

Short version urgent question is:
is a filter of calcium sulfite helpful/neutral/harmful in reducing radioactive particulate in hot/lukewarm water?

Additional questions:

- Does the answer to my question entirely hinge on whether the filter material is exposed to oxygen or not? If so, should I hope my chlorgon balls are oxygenated or vacuum sealed?

- Would a filter with carbon be much much better? Even though the water is hot or at least on the hotter side of warm?

- If it's phospholuminescent and it is collecting goodies, does that mean I should eventually be able to walk into my bathroom with the lights off and see the filter glow?

- Several sites are issuing and contradicting claims that calcium sulfite releases sulfur dioxide and this latter is a health risk. I have not been putting my attention n this because it seems that my maximum 15 minutes exposure to potential gaseous sulfur dioxide (and accumulating gamma activity from the filter) during the shower is not nearly as much of a concern as whatever radioactive isotopes I might receive from the water (I assume immediately through nicks and cuts, mucous membranes, and inhalation of vapor, but also I expect that I would then walk around with particulate on me that I could inhale or ingest later, especially on my hair - I have a lot of hair.) I have no asthma concerns but 5 distinct reasons why i would want to minimize my internal absorption of radioactive isotopes more than the average person. (Just pretend I am a fetus in Japan). Am I understanding the shower water risks correctly and are my weightings logical?

- Bonus question! I use cold water running though a standard Brita filter on my kitchen tap for everything else. I understand this filter is carbon, so, that means it helps, right? Fingers crossed :)

Thanks in advance for any help answering any of these!