I have neck pain and 2 lumps on my neck could it be thyroid cancer? Also back pain and cough since october and done light nausea

Possible. You need to consult a physician. These issues may or may not be related. The neck lumps could simply be enlarged lymph nodes due to infection of the lungs (explaining the cough) or something more serious.
Unlikley. Too many symptoms... Neck and back pain - highly unlikely to be anything serious and certainly not a common symptom of thyroid cancer. Cough?... Could be anything - viral respiratory infection/allergies. Lumps: anything larger than 2cm or presence for more than 2 weeks should be checked - see your local ent.