This might be the perfect time to create a design that incorporates your existing belongings into a harmonious whole. Volunteer to do the painting yourself, with a little help if you think they can/would do so. Maybe they would be willing to spring for paint and supplies if you did the work yourself. If not, price those items and save up for them. Get advice at the paint store.
I painted my own room for the first time when I was around 15, and had "helped" my parents paint other rooms at different times over the years. I've painted rooms over the years, and it is a little time consuming, but not hard. The hardest part is the prep, and the most fun part is seeing the color roll on and/or removing all the prep/protection to see the finished masterpiece; the most tedious part is cleaning up the painting tools afterward.
If you don't already know how, surf youtube and the internet to learn exactly how to prep/protect, tape off and paint a room. I suggest you use a neutral version of a color that looks great with the colors you love and whatever flooring is going on.
If you love blue and purple, beige and tan are neutral versions of orange and yellow, the complementary colors that will highlight them. Either one - or a blend of them - would probably look nice with a beige carpet. Grey with a lavender undertone is an on-trend neutral, and steel grey with blue undertones would go with blue - and would be nice with a carpet with more grey in it. Any of them would look nice with wood floors.
Going with neutral wall is smart. It lets you change up your style with ease, too. Your parents already know this, I imagine. Going with a neutral may appeal to your parents a lot - they may think "Hmm, when she moves out we can use that space without repainting it." Let this work in your favor.
A classy room usually has a neutral-ish wall and basic furnishings, and is tied together into a coordinated whole by sprinkling coordinated fabrics and objects through the room. My first house as a married woman had a wide assortment of ill-matching furniture styles and colors and a boring neutral wall color, but I got compliments every time people came over because of this fabric trick. I used super-inexpensive chintz fabrics that were very similar in color palette and pattern-size to what I already had going on. It made me feel SO much happier to be in my house after I did that. Before that, the mismatched styles drove me crazy. A few lengths of fabric, a few inexpensive chair cushions, and a couple of accessories and boom, it was beautiful and eclectic instead of mismatched.
You may find fabrics that focus on your blues and purples, and the greens that aren't your favorites will become less prominent.
If you create a simple design and a budget for it, your conversation with your parents may go a lot more smoothly than you imagine. They may be impressed at how much you can accomplish for so little, and get over their reluctance to help you. Maybe they spend a lot of money on your brother and are feeling like the budget has been stretched too far to take on another decorating project.
Good luck! And make your own luck by designing and planning ahead for a successful makeover.
Calmly explain to them how you feel without getting angry as they would see how mature you are and would definitely want to do your room. Maybe your parents think it's a priority to do your brothers room as he's the oldest so when you're slightly older they may be able to do your room as they will have spent enough money already on doing your brothers room. Or compromise and wait a few months or so and when they've saved up enough money they may be able to do your room and buy you new stuff for it.
So today, my brother got his room totally remodeled, kinda. He got a new desk, a new dresser, lamp, chair, stool, and decor. His room looks awesome. It matches and coordinates and all that. His desk and shelf are white and his bed and dresser are wood.
So anyway, his room is smaller than mine, my room is actually quite big. I recently got a new bedspread, and a few boxes that match.
I still have to paint my room. After my parents said we would, 7 years ago. I am 14 now. My brother is 17, and is a seinor in high school. He will move out soon.
I keep telling my parents I want to "redo" my room. I want things to match and coordinate. All the woods in my room are darker, but don't match. I also have an electric piano in my room. Nothing really matches. There's greens and blues and purples and pinks. I want blue, and purple. Well so I try to explain this, but they don't get it. I told my mom and she said "well I got you boxes for stuff on your shelf"
Yes well you can still see my crap everywhere.
How do I explain to them what I really would like to do without them getting mad? (Already have...)
Also, I cannot get new furniture.
Ps,
It really sucked watching my brother get an awesome room today, and seeing my room so, average. I know I seem greedy and ungrateful, but it's not fun. It wouldn't be for anyone.