Aww, it's tough when your family doesn't support you in your dreams. It's ok if they don't support you financially, but it's much worse when they don't BELIEVE in your dreams and don't offer any emotional/psychological support. I've been there many times...
I'm not a makeup artist myself but here are my two cents on your situation:
For learning techniques: take advantage of all the beauty "gurus" out there and scope out their blogs, videos, etc. More importantly take notes on the things that you agree with or would like to try out so you stay organized. That way as you compile more info, you can make yourself a "how-to-guide" for all the looks you want to be able to create.
Also, how about contacting a few local makeup artists in your area and asking them if you can intern for them? Offer them your sense of hard work and your enthusiasm to learn. Don't expect to get paid, but even if they allow you to tag along to a client session you might be able to learn extremely valuable things. Plus this adds to your credibility as a young makeup artist.
For building your makeup collection: don't ask for money from your parents. It's tough, but you might be able to find a part-time job in an unrelated industry - any service related job, like in retail or food services would be great. (I worked for Subway making sandwiches when I was your age; wasn't particularly fun, but any work experience is better then none). You can earn some extra cash from your job and more importantly also take that opportunity to meet people outside of school. Maybe this will be the start of your makeup clientele...ya never know.
You also can start out with a blockbuster style type of palette that has many lip, eye and face products all in one, so you can try out many different colors and finishes before you commit to more high-end items. For instance, if you can save just $50 (which I'm sure you can!), you can get this palette from Sephora with 72 eyeshadows, 28 lip products, 7 blushes, 18 cream eyeliners, 3 concealers, lip and shadow primers. This is a good way to get your hands wet, experiment, and practice basic techniques without having to spend a lot of money.
http://www.sephora.com/makeup-academy-palette-P381158?skuId=1534858
Making a career out of makeup: Trust me, a lot of us gals here probably wish we could work with makeup and cosmetics for a living too. In reality, it is a tough market out there, as it is for more and more professions. People like Michelle Phan and Wayne Goss are successful not only because they are talented at makeup, but also because they are good business people and marketers of themselves as well as their products. The truth is there are even more talented people than Michelle, Wayne, Lisa and all those gurus, but yet they might be essentially "starving artists" with little income. Why? Because being a successful makeup artist is not just about art. It's art + business. So I highly encourage you to not only focus on your makeup training but also to teach yourself how to be a successful business woman.
Finally, have you considered perhaps starting out your makeup career in stage makeup or costume makeup? There is a show called Face Off (google it for more details), where makeup artists (amateur and professional) compete to win $100k from Make Up Forever. Many professional makeup artists get their start in costume, film or theater makeup - including Laura Geller for instance. (She sells her own line of cosmetics on QVC and department stores) Heck, if you said "Hey mom I'm going to be working creating the makeup looks for The Walking Dead" or "I did the makeup for Cirque Du Soleil" or "I'm doing the makeup for this broadway play", your family might be able to more accepting of your choices to go into makeup? Not that you should do something just to please your family, but it can make a whole world of difference when they can accept, respect and even admire your pursuits and dreams. Plus, if you do start out in makeup this way, you'll meet sooo many valuable contacts in the industry and I'm sure you'll learn tons of skills as well.
Anyway, good luck to you Karson!!