1. Not a day goes by (ish) that any given programmer doesn't question whether they know what their actually doing or not. Run into a hard problem / something not working / something that takes more then 5 minutes to fix and even the best programmers question their abilities. What makes a good programmer more than pure knowledge is the ability to look past that noise; have confidence, focus, and work towards fixing the problem at hand.
2. Anyone good at anything didn't get good at it by doing it for a few hours and moving on to something else. Being good at something means doing it every day; at least a few hours a day, for years. Every new language you learn; every new framework you try means the same time commitment is required.
3. If you want this bad enough; if this is the career that interests you most - do not compare yourself to others. Do not worry about what your classmates are doing or the guy / girl in the next cube is doing. You do you. Keep plugging away and try your best.

Will your dreams of becoming a good programmer come true? I don't know. Will they? How bad do you want it.

As I explained before, all you need is passion. If you can stick to programming and constantly improve, you will be good in a few years. It's all about doing what you like and constant practice!

Also don't worry about your age and fears. You are not alone! Most people worry about their future. If what they decide is the right choice. If they are too late to start doing something. How things will work out later on. Will they be able to get a job? Will they be looked down upon? And so on. Don't worry. We are all human. There are people who start playing the piano at the age of 7 and drop it later on, while other people start their studies at the age of 60 and find the solution to an important problem. It might work out the other way around, too. It's your life, and that one life you are experiencing right now is unique. Do whatever the hell you like with it. Make sure you have fun. Try to live in a way which does not make you regret decisions. By the way, most people rather regret things they did not do than things they did do.

So, give it a shot. If you like it, congratulations, and good luck becoming successful (though the probability is high if you do something you like). If it's not the right thing, don't worry, it was a worthy experience and you can move on. Lately, I have been reading a Manga called "Denpa Kyoushi", which is all about doing what you like and going all out. It's a real motivation booster :D

Go and find yourself!