You are only being exploited if you: 1. Are "worth more" in the industry (you could get paid more for the same work) 2. Are unable to take another higher paid position for whatever reason.
Both of these items must be true.
If you have heard of others paying more, that doesn't count... the only way you can reasonably claim to be "worth more" is if you have actually been offered a position at a higher pay rate. Then you can either take that position, or work for yourself, or turn it down because you like your current team. A situation such as yours is only exploitive if the employer is underpaying you AND blocking your ability to transfer.
If it's too much to get everything done in 18 hrs / wk, then it doesn't get done. They can increase your hour cap or your deadline. These discussions are sometimes hard, but they're not complicated.
What you fail to realize is that you are, right now, gaining the most valuable thing you can: experience. Though most tech shops claim to be a meritocracy, you'll discover very quickly that experience is very highly valued by hiring managers... maybe even more than it should be. So you're making $15/hr, and could be making $20 / $50 / whatever. Treat this as a learning experience to sharpen your skills and seriously buff your resume.
You need to optimize for learning. NEED TO. This is the wrong time in your career to optimize for paycheck.