Relax! There's no sense in adding stress and anxiety about diet to your stress and anxiety about acne. Won't do you any good and doesn't address either situation. Where your diet is concerned, I'd certainly suggest talking to your parents about it if you haven't already done so and explaining why you'd like to alter your diet in order that it be more skin-friendly.
Although my situation is a little different, I can kind of relate. I'm unemployed at the moment and my parents do the bulk of the food shopping. Given that I'm not contributing as much money to the household as I was when I was unemployed, I'm not buying as much of my own food as I used to. So because I'm eating what my parents buy as well, I get whatever I'm given. But when I found out about intolerances I have and that there were things in my diet that triggered my acne, I explained it to my parents and asked that they not buy me those certain things. I provided them with alternative options that were easily accessible so that they didn't have to go out of their way. Fast-forward and, having seen the results the diet changes have made to my skin, they can quite blatantly see the difference it's made and the difference they're helping me make.
Obviously, I don't know your situation and how well you get on with your parents, etc., but perhaps a similar approach might help your cause. Regardless, it's not worth getting yourself so worked up about and you certainly shouldn't lose sleep over it.
In terms of practical steps when changing your diet, it doesn't have to be drastic and certainly doesn't have to be expensive. In fact, sometimes it's more about what you take out than what you put in. It sucks that, generally speaking, fresh fruit and vegetables seem to cost more money than junk food. That just seems to be the way these days. But if you can shop around and work out what's affordable, you could perhaps come up with ideas that are within your parents financial means.
The most important thing is to not get obsessed about it all. Be practical. I know that sometimes it seems easier to freak out and essentially be somewhat irrational about it - I did that for years! - but it doesn't get you anywhere. It's a waste of energy too because the reality is that the smaller practical changes have a far better positive influence on your skin, your health and your mental-well being. Once you start turning that cycle around it becomes positive, things get better and better, trust me on that. Don't let all this negativity and panic rule your thoughts so much, see if you can calm yourself down and worry about it less. Take your mind off your skin too, distract yourself with things you enjoy doing and see if you focus on happier things a bit more.