I'm on wk 3 of concussion? How much longer? Why can't I go back to work with headaches?

It may not be... The headaches that are apparently causing your doc to recommend rest. Rather the headaches are signs that your brain tissue is still healing, & hence, needs to be rested. Please ask your doc (neurologist?) to clarify this for you @ help you understand their thoughts on the criteria for you to start work again. Part time and light duty might be a good starting point.