Jen But I feel bad quitting
First of all, congratulations for making it.
I find it hard to say whether you should or should not keep it going, but I definitely do not agree that taking off the belt would be quitting: you set yourself an experiment of staying chaste for 2 weeks. Now the weeks are over, and you have succeeded, taking off the belt is what you had planned all along.
You could even argue that taking it off is part of the experiment, to see how that makes you feel. If you will play with yourself, and feel bad about it afterwards, you know that continuing on this path is the right way. You could even do another experiment on how long you can last before giving in. (Knowing that you will give in sooner or later, so it is not setting yourself up for disappointment, merely a test to measure your strength of will: you have been quite strong in these past 2 weeks, perhaps more so than you expected?)
On the other hand, if you do masturbate, it might be a bit of a setback, and you would have to start all over again. But I'm not sure how true that is, given that the urges will continue to be there anyway: it is not like you need to go through a hard period, and then it will get easier.
With school you wouldn't have to ask them to unlock you, but just wait a bit longer before locking it back on when you come back from school - that way it is not so obvious to them that you 'used' that time. But even now there must be times when you leave the house and it is taken off, so you could still do it that way, if you do decide to give yourself a break?
It is nice of your parents that they didn't attach conditions to the new phone; they are apparently content with the progress you are making at the moment. So don't start feeling obligations about that, and keep deciding for yourself what is best for you. I think that kind of pressure works counter-productive for you.