Firstly, please accept my heartfelt blessings that you be blessed from Above with a “Refuah Shelaymah” — a complete and speedy recovery.
Regarding your concern about the dots being a tattoo concern — the answer is “No”. The locater dots are there for only one reason: that the treatment should be as effective as possible, and that you become completely well and healthy. That differentiates them from other tattoos that are done for “cultural” or “social” reasons.
So please don’t give the dots another thought. Not only is there nothing wrong with having them, but it is even a mitzvah to wear this “tattoo”. Since the dots help protect your life and wellbeing, having them is a mitzvah of taking care of your health, as the verse teaches: “And you shall guard yourselves very well.” (Deut. 4:15)