Obviously you don't have a choice on receiving messages. But you do have a choice on how to read and respond. How about focusing on your own work and read the messages occasionally when you have extra time just to show that you care and you are trying your best. That's it. Mute it when you are working or taking rest. You have no need to do everything perfectly or exhaust yourself. If your boss question you something, just ask somebody relevant including your boss. Tell them you were focusing your work which is more important. What you do and why you are doing this is for the benefit of the whole team.