DD was tested for TB when she was a toddler, after being admitted to hospital with a chest infection. They did the mantoux test (skin test) after detecting an irregularity of some sort on the chest x-ray. It wasn't very pleasant, but we survived! 
As far as I understood it at the time, the doctors were concerned about a shadow on the x-ray and thought it could indicate TB, but weren't sure. That's why they did the mantoux test, in order to establish whether or not she had been exposed to TB. Thankfully, she hadn't, and the shadow on the x-ray turned out to be nothing to worry about.
So sorry that your LO is sick - it's so scary when they're in hospital isn't it, and very frightening when they mention things like TB? But please don't worry, as it may well turn out to be nothing at all. If it is TB, we were told that the treatment would involve a long course of antibiotics over a period of several months. Not sure about rest of the family, but presumably they would have to be treated too, due to the prolonged exposure.
Are you aware of any risk factors for TB for your DC? DD was considered at risk because she had travelled to visit her dad's family in a country where TB is prevalent, and due to an NHS error, she hadn't been properly vaccinated. But as far as I know, it really isn't that easy to catch TB through brief exposure - tends to be through prolonged contact with someone who is carrying it.
Please try not to worry - hopefully the tests will come back negative. Fingers crossed!