When I had a cortisone injection the doctor told me I needed to rest the area for at least 24 hours to allow time to heal after the cortisone injection.
The doctor also recommended to rest and avoid any strenuous activity for at least a month.
So you can return to some normal activities after 24 to 48 hours of the cortisone injection but avoid doing any activities such as lifting heavy objects for at least a month if possible.
If you can't wait that long you should just be careful to avoid any injuries or pain to your arm.
The cortisone injection usually takes at least a few days to begin working so it needs a few days to work and after the cortisone injection begins to work it can take a few months for the cortisone injection affects to wear off.