Shea Moisture products for hair, Cake Beauty for hair. The biggest thing is finding a shampoo and conditioner formulated for your hair type. If you can go to a Beauty Supply store, that is a great place to buy hair care products and they can help with selection also!
For oily and sensitive skin, Thayers is an affordable reputable brand that I swear by along with many others(American), HEEDA products I’ve come to love but I’ve only tried their for dry/combo/sensitive as that’s my skin type. The biggest thing I would say with skin care is looking for ingredients like Panthenol, Niacinamide, Vitamin K3, Hyaluronic Acid while avoiding extra ingredients and look for a lightweight formula like a gel cream or water cream. These are lighter on the skin and not as rich which typically is better for Sensitive skin.