No, I don't think you really have to worry for the sake of your child, but you need to see the doctor about this. Positive PPD tests usually trigger initiation of 9 months of therapy with isoniazid (no beer for you during that time) and follow-up chest xrays, but we generally do testing and treatment only in patients who have a high risk of exposure to TB or spreading it, i.e., health care workers, humanitarian aid workers, corrections officers, etc.
If you received the BCG vaccine, which is used in many countries with high TB prevalence, it may forever lead to positive PPD tests. If you live in an area with high TB prevalence, then go ahead with the BCG at the right time for your kid, but if not, then skip it. We don't do it in the US because of the low prevalence of TB, the variable effectiveness of the vaccine, and the fact that it will later be difficult to determine with PPD testing if the patient has been exposed to TB or if the test is positive just because of vaccination. Consult a doc in that area or a travel medicine doc stateside that can give you good advice on it.
The vast majority of exposures to TB don't lead to active disease, but the bacilli are walled off in the lung by immune cells, where a sort of mexican stand-off ensues. The TB is isolated and can't grow, but the cells can't destroy it because of the thick waxy coating on the bacteria.
There is no good blood test to see if you have active TB. There are sputum tests, which are stained for TB (acid fast bacilli, or AFB smear) or tested with immunological tests, but they take some time to come back (~3 weeks) and are not recommended in asymptomatic folks with normal chest xrays. They are generally not performed unless you have symptoms such as cough, shortness of breath, night sweats, unexplained fever, or chest pain, or have a cavitary lesion seen on chest xray (there is a form of TB, called milliary TB, that does not have this xray pattern, but can look like a regular pneumonia).
If you are immunosuppressed (HIV+, other diseases), then treatment with rifampin and pyrazinamide is recommended rather than isoniazid. This also changes the definition of a "positive" PPD test.
CDC Recommendations on TB testing and treatment
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