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The injury meant Terry missed the shock 3-0 home loss to Sunderland on Sunday, which highlighted how even champions and league leaders Chelsea were weakened by the absence of the England central defender.
Terry, 29, said he could no longer play through the pain of an injury which first surfaced towards the end of last season and said a lengthy break from football might be the only cure.
"It is at a point where I cannot carry on with it," Terry told Tuesday's edition of Britain's Sun tabloid.
"I used to be able to make it through games because the adrenalin gets you going and you blank the pain out.
"But now there is no decision to make. After games I'm in agony and not sleeping at all."
Terry, who will miss England's friendly against France at Wembley on Wednesday, was reportedly considering whether to fly to Italy before the end of the week to find a cure.
"I'm at my wits' end," he added. "I know I won't play against Birmingham on Saturday but beyond that there are no clues.
"It could be weeks, it could be months."
England coach Fabio Capello believes Terry has made the right decision to try to solve the problem for good.
"I read that he will be out for a long time. He played many games with injections," Capello said.
"I think his decision is good because he can't play every game with injections. He has to be fit for our qualifying games next year.
"Until now he didn't play for England this season because he wasn't completely fit. He preferred not to play so he could be fit to play for his club."
Chelsea have already been without Frank Lampard for much of the season and the England midfielder is set to miss two more weeks with a muscle injury.
The Blues are also without key midfielder Michael Essien, who has two games to run on his suspension after receiving a straight red card against Fulham last week.