The North Shields-born star had been due to play the O2 Academy in Newcastle on Tuesday and Thursday, February 4 and 6.
They will now take place on Monday, February 17, for the first date and Wednesday, February 19, for the second, with all existing tickets to be valid.
Anyone unable to make those dates will be able to get a refund at their point of purchase.
The decision follows on from plans to reschedule other shows last month.
In a statement, Sam said: “I’m gutted to have to do this again.
“I’ve had an absolute shocker with my health.
“It’s been a series of unfortunate events this last month with chest infections, laryngitis and a family bereavement, and now I’ve come down again with tonsillitis.
“I’m raging, all I want to do is get back out and sing, but I just can’t.
“I know this is massively inconvenient, I can’t apologise enough,
“I’m so sorry. My immune system is totally **** at the moment, I’m doing everything I can to combat that.
“The only thing I can do is tear the ******* roof off when we reschedule again.
“It’s a big year ahead, mental things are coming, I just need a bit more time to heal.
“Thanks to you all for sticking by me, I couldn't ask for better fans.
“Love you all. Sam x.”