Can medications only resolve spine tb lesions and cold abscess?

Yes many cases can: Be treated with medication as long as there is no spine instability and/or neurologic deficit or imaging consistent with imminent instability and there is no significant abcess.

Possibly : Surgical indications for vertebral/spinal TB infection (pott's disease) includes: progressive neurologic deficit, severe kyphosis, progression of kyphotic deformity especially with spinal cord compression leading to neurologic deficit, instability despite adequate medical treatment, pain related to spinal instability. Surgery is also recommended for abscess, especially cold abscesses of tb.