Thanks for your question on Healthcare Magic.
I can understand your concern.
Yes, you should definitely take anti tubercular drugs.
TB PCR (polymerase chain reaction) test is highly specific. It's specificity is almost 100%. So no chance of false positive report.
You might be having mixed infection (tubercular and bacterial).
So with antibiotics, your bacterial part is improving and hence chest
x ray is also improving.
Tuberculosis is basically a chronic disease.
If don't take treatment at present, it will show after 1-2 months.
So even if you are improving with anti tubercular drugs, since your TB PCR is positive, you should definitely Complete the course of anti tubercular drugs.
Hope I have solved your query. I will be happy to help you further. Wish you good health. Thanks.