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Dirty looking neck could be acanthosis nigricans
, Darier's disease , CRP etc. It is better to get a dermatology consultation to diagnose the condition. Like wise the spots on the face also is difficult to diagnose from the description. A photo would have helped.
Acanthosis nigricans is quite common in obese
individuals and it cannot be removed surgically. Definitely exercise and weight reduction will help in this condition. But a final call can be taken only after confirming the diagnosis.
Hope this helped