I agree that you may need to start washing it at least twice a week. Maybe every 3 days.

I use coconut oil on my skin, but I have fine hair, and if I use it on my hair, it just gets stringy and gross. Instead of the oils, you might want to try co-washing, which is washing your hair with conditioner, and saving the hot oil treatments for once a month or so. I think heavy oils work better for those who either have straight hair or are curly 4s. The rest of us it just weighs our curls down a lot.

I am uncertain how long your hair is, but it sounds like you are expecting way more curl than is natural to your hair. It's okay to be a 2! I wish my hair were long enough for some of the pretty wavy styles I find online, like sock buns (makes perfect waves). Thicker braids can make some pretty waves. I also saw a tutorial where someone put a headband on, wrapped the hair around the headband, and slept on it. If you search Youtube for sock buns and headband curls, you find those.
Averages out at 2b, ranges from 1c to 3a, very fine
Mane 'n Tail co-wash + leave-in
Clarifying shampoo every few weeks
Lavender Allergy