You might be having a combination skin(dry with oily t zone). To keep your skin well hydrated use a mild face wash and a moisturiser well suited to your skin type. The black spots that you have mentioned might be black heads. Comedones and acne
are quite common in adolescence. So don't worry. You can get them extracted and can apply anti acne gel to prevent further occurrence( like application of adapalene
gel at concerned areas in night). Hope that solves your query. Take care.