Exactly, tea tree oil is great for treating flakes due to dandruff caused by a bacteria, but tea tree oil is drying so if your scalp is dry it will make it worse.
Personally my scalp was dry and I had allergies. The coconut oil or olive oil soak sounds great, but you should also pay attention to what products make your irritation worse.
3C/Fine to Medium/Low Porosity/High Density
CJ Gentle Cleansing Shampoo
DB Pumpkin Seed Curl Moisturizing Conditioner
CJ Smoothing Lotion
Queen Helene Sculpturing Gel & Glaze
No Salts, No Waxes, No Butters, No Heavy Oils
No ACV, No Saponified Oils, Protein Sensitive