If your doctor thinks it's necessary to do more investigating, then I think that's a good thing. To many doctors do too little testing.
The lump is probably enlarged lymph nodes. Has he ordered a chest x-ray or anything else for the TB? Has she had other symptoms?
I would suggest taking a list of your questions to the office visit and make the doctor answer them. Particularly, what he is looking for in the FNAC, what happens if it's negative or positive, what treatment she should receive, what the prognosis is, what other tests she should have, is she contagious, what are the odds that the TB test is wrong, what other possibilities are there, etc. You will feel much more in control and able to make decisions if you are fully informed.
Be nice, but firm when you ask these questions and don't let the doctor dismiss you. After all, you are paying him, right?
Let us know what the doctor says.