Brown dots top lip border - what can I do to have it removed? (Photo)

I suggest consulting with dermatologist to get a more accurate diagnosis and treatment for the brown discoloration at the vermilion border. That part of the lip is notorious for getting excessive sun exposure because of how it projects.
It’s most likely related to melon release which can be a response to minor injury such as stimulation from treatments, sun exposure, genetic variance and sometimes there is no explanation.
IPL treatment directed specifically for brown spots it’s probably a good fairly safe way to approach it. depending on the underlying ideology hydroquinone may be helpful. Hydro quinone is affective when the number of melanocytes remains constant but each melanocyte has been stimulated to create more melanin.
Aggressive use of high SPF sunscreen and avoiding sun exposure by wearing wide rims hats and simply not being outside when the sun is very strong or limiting sun exposure in general is probably your best option.
Best,
Mats Hagstrom MD