Hi I'm also a nurse. During my preg I spoke to the nurse doing the rosters about night shifts and didn't have to do any. The staff were very supportive too in making sure I didn't get a too heavy load of patients, sending me to first meal break, little things like that.
Are you permanant night shift or rotate? If you feel you can't cope for the rest of this week of nights maybe just pop into your GP and get him/her to give you a certificate.