Will tactupump help with my hyper-pigmentation from sun-damage and dark acne scaring or will it hinder it?

Neither: This is a mix of benzoyl peroxide and a retinoid which you could get cheaper on their own. It will not touch the scars or hyperpigmentation from old lesions, but it's okay for keeping mild disease at bay. Best wishes.

Exactly which pill?: This product combines benzoyl peroxide with adapalene. Adapalene is better than tretinoin [RetinA] and is better tolerated. It recently was introduced OTC at $12 for 15Gram tube. It helps acne and may reduce pigmentation. Birth control pills are not all the same. Yours might make acne worse and might increase pigmentation. You might benefit from oral therapy, a change of birth control, hydroquinon