If you head aches are tolerable, stay away from prescription pain meds. The vertigo may need to be assessed by a vestibular specialist. It does not sound like your doctor knows much about concussion.

If you can work without putting yourself in danger from the vertigo or poor reactions, it's a shot you will have to make. Working will not make you symptoms permanent. It will just slow your recovery. You also need to not put yourself at risk of another head impact.