I can say that some companies do pay injured workers for the time that they spend at doctor's offices for treatment of work-related injuries. But, not because it is a legal requirement--more of a moral obligation in the cases of which I am aware.
Many states would require that the company's workers compensation insurance pay the worker for this time.
So, the first thing you probably should do is talk with your workers compensation insurance broker/agent/carrier and ask them what they cover in these regards.
Hope this is helpful.