You need to treat the infection immediately. You will die if you wait months until consolidation.
Although it is true that infection should be dealt with promptly, it is a little more nuanced than that.
infection can be on a spectrum of severity. Yea me should suspect infection anytime there is persistent drainage from a surgical wound. the first step is to treat with antibiotics and monitor signs of deeper infection on x-rays.
Lengthening can occur in the face of low grade infection, but once the length is achieved, if the symptoms persist, the surgeon should consider a washout and an exchange nailing with an antibiotic cement coated rod.
thankfully it is quite a rare scenario,