Lambekel,
Sorry it took me so long to respond. I have just joined this site. I doubt very much that your child developed TB from this unfortuate incident. It was more likely a virus because of how rapid the symptoms came on. TB takes 2-10 weeks to develop symptoms and usually is transmitted by a cough not spit. However, it is possible to get it that way. Viruses usually can come up quickly. It may have been Adenovirus or some other such virus. What does the cough sound like and does he still throw up with it? Pertussis is also going around. I don't know if your son has been vaccinated for it. Did the doctor take a culture from your son? I hope he feels better soon.
mkh9
Hello and hope you are doing well.
Understand your predicament. As suggested tuberculosis is usually a chronic disease. Here the PPD is positive. This is correlated with clinical symptoms, like cough, evening rise of temperature, weight loss and blood tests, which will show a raised ESR and increased lymphocyte count, if it is an active infection. So, if his symptoms are not improving with the medications given, then you can think of ruling out tuberculosis.
Hope this helped and do keep us posted.