Welcome to HCM
Your wife is suffering from Tuberculosis
and is already under treatment as you said there is no sputum production so such cases are Sputum negative for AFB.
Even if it is positive in most cases it becomes negative in 2 months of 4 drug treatment.
She is feeding her baby hence it is important to consult Pediatrician
to safe guard the infant may be by vaccine
and if appropriate chemoprophylaxis
You should go for repeat X ray and blood test
to see improvement in x ray and there is nothing else which is missed.
In most cases cough should subsides in 3 to 4 weeks time depending on result of fresh investigations cough suppresing drugs may be given for her.
There should not be any risk of spreading the TB bacteria ( This is not Virus).
I hope she takes regular treatment and at least for 4 more months she will be free of TB.