I am no expert on how things work in the States, but the bottom line is that you will need to find a way to fund training. At 16, you could start learning to fly now, and in the UK you can get a PPL issued at 17. I think it's the same on FAA licences but do some research there. That's the first step you will need to take, but it might be more cost-effective to wait until you want to start a more continual training programme towards your CPL. Before you start training, you will need to get a class one medical certificate from the FAA, something you will not be able to fly commercially without at all.
At 16, you are still rather young, relatively speaking. My advice would be to continue your education - the more qualified you are, the better back-up plan you will have, and the more you will be able to take with you into a flying career. An aviation degree would be a good way to go about that, but most importantly do something that will reflect decent grades and that you will enjoy.
In the meantime, by all means get up there and flying! Perhaps do some gliding - it's a fantastic way of building a hugely solid foundation for the rest of the flying you will do (plus it's cheaper). Eventually, as the US employment market is different to Europe, you should anticipate the need to build hours for a couple of years as an instructor, which may well be poorly paid, but it gets the hours. Try to get hold of pilots currently training, a few airline pilots and people in similar situations to yourself to give yourself access to a massive source of relevant information and experience. Hopefully that's more useful.