Waxing doesn't cause dark skin spots in itself. But waxing exfoliates the top layers of skin, potentially leaving skin more vulnerable to the sun and tanning beds.
If you are taking antibiotics, on birth control or hormone replacement the skin can become sensitive to the sun (photosensitivity), which may cause it to change in pigment. If you are on one of these drugs, then I would suggest applying a sunblock daily to your skin, whether it’s sunny or not. Stay out of tanning beds, they’re not good for you anyway. But if you must, physically block the area that got waxed with a towel.
If you don’t see a change in your skin tone after using these precautions, see a dermatologist about what options you might have. In the meantime, use a concealer a tad lighter than your skin color and then your foundation to blend in the dark skin tone.
Other hair removal options like threading and sugaring, also take the follicle from the root but are less exfoliating and much more gentle on the skin.
Other issues from waxing like ingrown hairs, pain, bumps, bruising may also occur.
Cleveland Clinic. Is medication making your skin sensitive to the sun? Updated July 21, 2020.