I would be increasing my bloodwork, more biweekly tests with more blood panels
and a baseline of various cancer markers. I've commented a lot on this for colorectal cancer diagnosis and before any treatments; there are also a number of organ cancers that can elevate CEA. Hopefully you have a CEA transient or relatively benign condition, but higher and longer means more cancer concern, more pressure to definitively rule out other causes. Sometimes the cancer is hard to image.
I could give many concrete examples here, that CEA due to colon cancer definitely did rise that fast, or faster. In fact, oddly enough, I've been personally confronted with elevating CEA numbers like yours, twice. One going exponential (at dx), faster, and the other stair stepping (nodes) every 8-12 wks. We did extra homework and it paid off.
Inflammation can be tested for (hsCRP and ESR), and there are other cancer markers that would allow better definition if you are in situation that hasn't yet become imageable. I would be getting second opinions lined up, doing some homework. Appointments can be cancelled, but lead time becomes precious if you are going hot.