Yes, lack of money is a big stressor. I am wondering if your parents had some big financial loss and that's why they had to move and are now really tight with their money. (I know folks who lost a lot in the stock market, for example. ) And they are trying, albeit without success, to keep their money worries from you.
I honestly think most parents try to do the best they can for their kids. As a mom myself, I am thinking your parents are trying to give you good things. Wow, a private school? Most kids would be thrilled for that opportunity. I can understand why you would feel upset that now you can't have all the expensive things the other kids there have, but...... Would you rather go to a public school?
And getting a job would be helpful to you in more ways than one, if you can get one. Jobs help us to mature, allow us to see what our skills and interests are, give us something to put on a resume, and of course, allow us to have some money. I'm not sure I see your parents as being mean or wrong in asking you to see about getting one. I know some parents will not buy their kids something like expensive (name brand) shoes unless the kids contribute money toward the cost, if only by earning it by doing chores.
Please remember that you are used to living a grander lifestyle than many folks, so you are seeing the belt-tightening as really difficult to adjust to. A number of kids have always had to live on a tight budget.
That's my two cents' worth, anyway, as the parent of two young adults.

I suggest you try to cooperate with your parents. (I know that's not likely what you wanted to hear, though!

)
P.S. One day I was walking behind one of my sons, and it dawned on me that all the clothes I had on were from thrift stores or K-Mart (seriously), while he was wearing all Ralph Lauren attire. (Well, at least we got most of the items from TJ Maxx or some discount place!) And he was texting on his smart phone, while I was getting by with a basic cell phone.
But I am used to living a very modest lifestyle, so I don't feel deprived at all.....Please consider that. Okay?
Getting to your question, yes, we have talked to our sons about our financial situation. Perhaps if your parents haven't brought the issue up, then you can approach them about it with concern and caring. I doubt they are just trying to make your life difficult, but they really wish things could be better for you, like they were before.