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I dont think there's a single lotion or body wash that can handle all these issues. For ingrown hairs, I'd recommend using cotaryl cream and glyco 6 for a good aha bha body lotion to deal with pigmentation and tan. Chemist at play is a decent body wash for this, but it works slowly
You can start with an exfoliating body wash like chemist at play or be bodywise, that should take care of most of the concerns you mentioned like ingrown hairs and tan. Use benzoyl peroxide for body acne and a targeted lotion for pigmentation. Lotions are more effective than body washes since they stay on the skin for longer
I'm not looking for a single product that solves all these problems, I just want products that deal with specific issues
I've been using the daily exfoliating body wash by chemist at play for a bit now, and it's helped with acne, ingrown hair, and a bit of tan so far
For back acne, use a benzoyl peroxide body wash, benzoyl peroxide cream at night, any antifungal powder like candi gurd, and suthol when you're going out, especially in summers
You can use glycolic acid as a spray once a week
Chemist at play is a good option, the orange one
I'm really lazy and this fuss free routine has worked amazingly for me - I use dermaco salicylic acid body wash daily, dove exfoliating body polish weekly, vaseline gluta hya body lotion, and chemist at play lactic acid roll for underarms, elbows, knees, and inner thighs to reduce darkness. I also get waxed monthly and try to avoid using razors unless it's an emergency
For body lotion, wishcare aha bha body lotion is a good choice. For body wash, chemist at play exfoliating body wash is nice, use it with an african net or a silicone brush
For body acne, I found arata's 1 percent salicylic body wash to be really good. It's also super gentle on the skin and leaves it very smooth