when I turned 16 I started working for a chocolatier restaurant for barely above minimum wage.
In most jurisdictions, 16 years is old enough to work part time. You were paid above minimum wage which means the employer is 100% within their rights and responsibilities. If you can prove that you were paid less than an equivalent employee at the same time/ location/ shift for clearly discriminatory reasons (female, black etc.) then you may have a legitimate complaint. Being paid less than other employees that have 10 years experience and a relevant college degree doesn't count, they are not "equivalent" to your position. You mentioned that you compared your pay to "other professionals". At 16 you are not a professional - you are barely qualified to answer the phone.
Employers have no obligation to pay any "going wage" - they have a legal requirement to pay the minimum wage. Employees have the right to not work for that employer. You appear to have exercised that right by quitting.
How do I tell my boss that I need the money back that she never gave me.
That's quite a sense of entitlement. Unless your boss agreed to pay you $15 / hour and withheld $7 for questionable reasons you get nothing "back" as it was not yours to begin with. Your employer offered you a job at a certain rate, you accepted. That this rate was below market is your failure for not researching what that job normally paid for a person with your qualifications. Again, you don't compare yourself to a trained chocolatier, you would be looking at the entry-level zero-experience wage, and I'll bet that's right around the minimum you received.