Hi user
I'm really sorry it was not better news
scream, shout, swear, throw things... Whatever you need to do! We are pretty much unshockable 
Hopefully someone will be along later to help as I don't know much about breast cancer. But I didn't want your post to go unanswered.
I thought the same about stage III. They will not usually say someone is "cured" of any stage of cancer, because really the only way to know your cancer was cured is when you die of something else. It can lurk and reappear even many years down the line (though that's very, very rare).
Even stage IV cancer can often be controlled for years, though it's only "curable" in very specific circumstances and that's a recent development.
Do you have a breast care nurse? Can you ask for some clarification?
Triple negative is a bit trickier to treat because Tamoxifen and Herceptin are both useless against it. But plenty of progress is being made in triple negative breast cancer treatment too.
Have they arranged further tests to identify the chest lump?
And do you know what cancer you are having? People on here generally seem to have some combination of F, E, A and C and/or docetaxel or paclitaxel. So if it's any of those you're in good company
but some people have had other potions too so there's bound to be someone with some experience!
Losing your hair is not much fun, but you will cope with it, and maybe even manage to laugh about it sometimes 
Try to take it step by step. When is your next appointment? Just focus on that. Try to forget about all the future treatment stuff for now. You're in shock 
This was all a bit long and rambly so I will stop before I get any more carried away.
I hope that you managed to get some sleep.