Does the blemish treatment work on pigmentation caused by UV rays as well?

After spending a lot of time outdoors during the summer, small pigmentations that weren't there before started appearing around my cheeks and nose, so I am looking into blemish treatments. Although I applied sunscreen consistently, I often missed reapplying it in between, so I suspect the spots may have been affected by UV rays.

One or two are relatively clear, but the rest are blurry and spread out, so I don't know how to manage them.

Would the blemish treatment be effective for this type of pigmentation that developed after UV exposure?

I am also wondering if I should wait until my skin has sufficiently stabilized before undergoing blemish treatment. I would like to know if blemishes can darken again if proper UV protection is not maintained after treatment, and what kind of daily care is important to prolong the effects of the procedure. Moving forward, I would like to focus on prevention as well.