Knee vs back?
From this description, it is hard to say for sure.
Your prior knee event suggests maybe and injury to the soft tissues outside, or inside the knee. The burning and sharp pain up leg may not fit well with this, yet a more detailed history and physical exam would be useful with your PCP, an orthopedist, or Physiatrist.
In meantime, consider anti-inflammatories (if ok for you to take), ice, rest.