Beta-carotene - Carotenoids, in particular beta-carotene, much like melanin, are antioxidants. There is a reason you will see girls clearing their acne by doing several tanning sessions. As an example, though, I would not suggest doing this as it just ages your skin, only for you to breakout when you stop tanning. The reason one would want to use beta-carotene instead of lycopene or astaxanthin is that beta-carotene has the added benefit of being converted into Vitamin A, which is anti-inflammatory and reduces sebum production (it's also what Accutane is based on).
Zinc - Zinc is very effective at reducing sebum production, which is what causes acne and breakouts. In this study they used zinc gluconate in particular to cure acne. You will also be able to find many Redditors who have found great success with zinc gluconate. It is important to note that if you take it in high doses for prolonged periods, you need to supplement with more copper and iron. If your hair starts shedding, then you're likely low on copper.
Vitamin B5 - While not as popular or effective as zinc, it is still very effective at clearing up acne. B5 does this by reducing sebum production much like zinc, though to a lesser degree. Pantothenic Acid-Based Dietary Supplement in Subjects with Mild to Moderate Facial Acne
Other supplements for skin:
Lycopene and astaxanthin - Also antioxidants, though I primarily use these to get a red undertone. However, I do feel like these have been overhyped by TikTok.
Hyaluronic acid - In my opinion, the best supplement for skin. It makes your skin more hydrated. I take 600mg every day.
