Don't use the coconut oil!!! It's too heavy for acne prone skin and doesn't allow your skin to breath. Use a moisturizer that is oil free with an minimum SPF 30 that is made for oily skin.
I'm a licensed esthetician so let me see if I can help. If you have oily skin, you want to use a gel cleanser. It's better at removing the excess oil where as cream based cleansers are for dry skin types.
Acne happens for a number of reasons. Hormones, clogged hair follicles, too much sun, and stress and diet as previously mentioned to name a few. It sounds like you have grade 2 acne in your t-zone area which is common. The key is to balance your skin.
Drinking lots of water is a great start, and next you need to find a good cleanser to use in the morning and at night. A professional product with active ingredients like salicylic acid and benzoyl peroxide will help remove the oils and dead skin clogging the hair follicles causing the closed comedones, and the benzoyl peroxide will kill the bacteria should those become red and irritated. The salicylic acid is a chemical exfoliant and will dry the skin causing you to feel activity and experience some peeling but that's normal until your skin builds up a tolerance to it. Usually takes 5-8 days of continuous use. You can use a light moisturizer after you tone but make sure it's made for acne prone skin. Look for the word "noncomedogenic" when looking for skincare products. I can recommend products if you're on a budget.
Most importantly, protect that beautiful young skin with no less than a moisturizer with an SPF 30. If by chance you have acne scars as a result, the SPF 30 will protect your scars from them getting darker and driving the pigment into the dermis causing permanent scarring.