My mom skin tested positive for tb. Is it safe for my 6wk old baby to be around her?

Probably. Your mom needs a chest xray, to make sure she doesn't have active tb. (a positive skin test does not necessarily mean you have tb.) if the xray is negative, don't worry about your baby - but your mom needs to see her doctor, who will determine if she needs treatment, or if the test is a false positive.
Positive TB test. A positive TB skin test or TB blood test only tells that a person has been infected with TB bacteria.  it does not tell whether the person has latent TB infection (ltbi) or has progressed to TB disease. Other tests, such as a chest x-ray and a sample of sputum, are needed to see whether the person has TB disease.A new test called quantiferon-tb gold is helpful at diagnosing tb.