| "A club I swim at pays well, but the job seems so boring...I'd like to have something really benfitial for helping me figure out what I'd like to do for a career, like an internship or something."
In general, people don't get paid internships until they have either considerable education in the field offering the internship (and "considerable education" means that they typically have completed their junior year in college) or have skills at the level of what a person would have if they were close to entering the field.
Typically, the way that you get such skills is by volunteering. For instance, if you wanted eventually to get a job in a computer field, you could volunteer now to design webpages for nonprofits or school clubs; if you were interested in media internships, you could do lots of work --major stories of the award-winning type-- for your school paper or community paper that doesn't pay.
Also, working a job - any job including the boring jobs you're looking down on -- helps demonstrate the kind of self discipline and responsibility that would make employers be open to offering you an internship, something that costs employers a lot in supervision time, not just the salaries they pay. Consequently, it's not easy to get internships of any kind, particularly when one is a high school student. It's not even easy when one is in college.
All of this comes from my former experience recruiting and hiring interns. | 
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