Going with the title of your thread, it doesn't have to be completely an either/or matter.
While you need to look after your well being, and need extra consideration from LordL and anyone else who would be in your home more than briefly right at the present, you could discuss what special considerations or restrictions would be needed from your friend in order to minimize the anxiety and discomfort you have which are currently exacerbated as you work through the best medical path.
Your friend, by staying with you, would be able to conserve whatever is available gas for his family's generator rather than using it for his commute to and from work for a week.
If you can be clear and direct with your friend about what you need now (quiet, privacy, etc) and ask if that is acceptable to him for his stay, your friend's emergency needs may be mitigated by staying with you, impacts on you could be mitigated by being direct about your own needs. It may or may not be that your friend then decides to pursue a different option than staying with you, or stays only a night or two, or does indeed have a need to stay closer to his work which is great enough that he would happily, quietly couch surf for a week as unobtrusively as possible.