M. marinum is likely in most aquariums. It is also found in swimming pools (no longer common with chlorination) and most bodies of water that are relatively stagnant.
This family of bacteria has many species. Not to scare you but Tuberculosis and Leprosy come from this genus.
My daughter had a M. avium infection when we had several parrots.
If your hand turns out to have an M marinum infection, it likely entered from a pre existing cut. It may take several weeks of specific antibiotics to heal the wound.
While I am not sure I doubt you can rid the tank of the organism.
Hope it gets better soon.
This is a pretty thorough article:
https://www.tandfonline.com/doi/full/10.1080/01652176.2018.1447171