Coding slower for one month probably isn't the end of the world. For emails, tell people about your arm issue and ask them to have some patience with you. Try

Coding slower for one month probably isn't the end of the world. For emails, tell people about your arm issue and ask them to have some patience with you. Try and use voice tools to write out messages where you can. Depending on what kind of programmer you are, try and focus more on the things you can do without much impact: perhaps planning and diagramming out systems on paper, doing research, or doing some graphics related work. Hopefully your arm is ok.