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There are several possibilities to consider in this situation, and both doctors have stated correct possibilities.
A low hemoglobin can occur from bleeding from a variety of underlying causes or structures, such as cancer, ulcers, or diverticuli. Some of these are more worrisome. Using any blood thinner will increase the risk of bleeding from any of these underlying causes. The elevated CEA can be due to cancer, so can also be a site of blood loss.
It is also true that a definitive diagnosis can only be made after further evaluation. A bone marrow can help to clarify the cause of the low hemoglobin. But another approach would be further evaluation of the colon, such as with a colonoscopy or upper GI endoscopy.
Have you had a colonoscopy or endoscopy?
Was the hemoglobin and the CEA at the current levels when the colonoscopy and endoscopy were done?
If the CEA was not checked prior to the colonoscopy and was found to be elevated subsequently, then it would be reasonable to consider another colonoscopy. You are correct about the normal range for the CEA in smokers and non-smokers. There are many different possible causes of an elevated CEA, and if there is no evidence of colon cancer on colonoscopy, then there is no reason to repeat the colonoscopy as long as the CEA is not increasing further.