The short answer is yes, however it depends if your injury will put you at risk of your own safety and the safety of other. Also, continuing to work might delay your recovery depending on what kind of movements are required of you at work. There might be some modifications that your physiotherapist will advise you to do such as maintaining a good posture and proper biomechanics. Modified duties can be an option for some individuals. For certain types of tendonitis, a brace could be of benefit to offload the tension placed on the tendon and disperse the force (i.e elbow brace). A brace can help the individual continue with theirs tasks with less pain. Also, pacing a task can help tremendously too.