I Have A Small Spot In My Chest And My

I have a small spot in my chest and my blood test is positive.. I am exposed to tb from my roommate. Doctor suggested me to go with three sputum tests day by day early mornings. I am exposed very recently. Will it be cured? So my tb is in active or inactive? I have no cough no symptoms other than mucus in my throat and weight loss of 2 lb with in 2 days.