Your hair actually looks a bit like mine. I'm 2b too. I know exactly what you mean about it being unpredictable. I never know what I'm going to get day to day. I wish I had a stronger curl pattern, but I guess it just isn't in my cards. So I just go with it like Claudine said.
Going sulfate free left me a bit greasy at first too, but my scalp adjusted after a few weeks and now as long as I massage/scrub my scalp really well and rinse really well, I'm good, What do you use to wash your hair? In the summer, I always use a sulfate free shampoo (DevaCare low-poo) and follow up with a rinse out conditioner. In the winter when it's really dry out, I wash with straight conditioner (cowash) most of the time (Suave Naturals Lavender) and skip the low poo. If you're cowashing, maybe try a sulfate free shampoo instead if you're feeling greasy. And make sure you're really massaging/rubbing your scalp and rinsing well. That made such a huge difference for me when I started out. My DevaCare low poo runs about $18 for a 12 oz bottle, but I only wash 2-3 times a week and I only use a small amount each time, focusing most of it on cleaning my scalp. That bottle has lasted me a year and I've still got at least another 2-3 months of shampoo left in it. You can probably find less expensive low poos out there though. I'm a little more restricted because I have to find wheat free products.
Also, regular trims really help me out. My hair starts acting really funky at about 11 weeks, so I get a trim every 12 weeks.
Hair Properties: 2A/2B, Medium-fine, Normal porosity, Normal elasticity, Medium density
Low Poo: DevaCare, Yes to Cucumbers
Rinse Out: DevaCare One Condition, Yes to Cucumbers
Cowash: Suave Naturals Lavender
Curl Cream: AG ReCoil, Organix Moroccan Oil Curl Cream
Gel/Mousse: AIF, AIA Curling Jelly, Sweet Elixirs Flax Seed Gel w/ Mag Sulfate added, DevaCurl Frizz Free Foam, Aquage Uplifting Foam
Protein: Spiral Solutions Protein Spray for daily use