Had a doppler for the carotid arteries and the conclusion is:accelerated blood flow, reversed blood flow above the carotid bifurcation?is this serious?

Depends : The reversed blood flow in the carotid usually indicates a narrowing in the vessel closer to the heart. Your symptoms usually indicate if treatment will be needed. At a minimum medical treatment is necessary. For most people the condition ends up in surgery. There needs to be investigation to determine the cause.

Probably yes: You should consult a vascular surgeon. While this could be serious, it could also be a false positive finding. It is not something that you should handle over the iinternrt.