Latent tb infection

I got accepted to nursing school and got tb skin test as one of the requirements. To my surprise, the result was positive. Then the chest xray showed minimal infiltration. I’m perfectly healthy, no coughing or fever, so the doctor determined that I had latent tb. Since it’s not contagious, I thought it would be fine for me to get treatment and go to school at the same time. But the school contacted me a week later and said that I couldn’t because the hospitals they sent students for clinicals didn’t accept students that haven’t completed latent tb treatment especially during this time.