This happened to me recently. It turned out to be the shampoo, which was Head and Shoulders Dry Scalp. I use it during the winter because my scalp gets dry and itchy. When I switched to it this winter, I noticed that my hair felt greasy. I didn’t immediately associate it with the shampoo since I had used H&S before. So, I washed more frequently, which just made the problem worse. Finally, I decided to see if it was the shampoo, so I got a clarifying shampoo. That fixed it.
I still don’t really know what happened. I guess H&S changed their formula sometime over the past year. I did consider that it may be related to the phosphate ban, as removing phosphates from shampoo could have that effect. But, that is 100% speculation. After I resolved the greasiness, I decided to use a good moisturizing shampoo instead of H&S during the winter. I haven’t had the problem since.