Dear Sarah (from Detroit)
If you love Calculus and AP Chem then you are certainly on a classic path to head towards Engineering, and especially Chemical Engineering, as a major at college. Given that you love make-up and hygiene products (and who doesn't!), you should know that, for decades, Chemical Engineers have been hired by all of the major U.S. companies whose businesses are focused on those products. I am thinking about Proctor & Gamble, L'Oreal, Clorox, Unilever, and many more.
Make-up and hygiene products offer a rich set of problems for engineers, from surface chemistry (to reflect light away from skin imperfections, for instance), to biochemistry (clearing up acne), to materials engineering (balancing a soft but strong toilet paper. The key core competencies are chemistry, engineering, and math (you have to model and analyze the product designs you are considering).
As a chemical engineer I may be a bit biased, but I would recommend that you consider a chemical engineering program. First, packaging is a more narrow focus and it is not a major at many universities. Second, post-college, you will have a career spanning about 45-50 years and you need a broad-based education to make sure that you have the background for whatever you do over that long time (and it's not likely to be just one job). Third, many people come into college with one career aspiration and then get inspired to do something else. So you want a degree that allows you the breadth to prepare you for any changes you end up making in your focus without having to change majors.
With respect to environments, this will depend on where you are in the design chain. You may be in a laboratory if you are more focused on the chemistry of these products. You may be working in a pilot plant, running your own tests on a small-scale and then analyzing them. Or you may be working on the (large-scale) manufacturing process itself and having to trouble-shoot quickly as problems arise (rather like being a first responder). Each of these environments are quite different and will reflect the activities relevant to that stage of the process, from lab bench to full-scale production. Then hopefully, some day you see the product you worked to produce on supermarket shelves- how exciting.
Finally, as any one who reads my answers to Engineer Girl knows, I also recommend that you ignore the salaries. You need to do what you love first and foremost. Love what you do. No amount of salary can make you love your job. You clearly already have passion, harness that instead.
Good luck and keep up those math and chemistry classes.