First Haley, hello and welcome! The fact that you are here asking such questions at such a young age and lack of experience is an extremely positive sign. Keep it up and remember knowledge is power.
Now, to answer your question. Typically, I would say absolutely not, you shouldn't do this and this could ruin your career etc etc.
Since you are 17, he seems like a jerk and the job will likely have no impact in your future make sure that it is epic and represents what all of your co-workers certainly want to tell this person.
I would also recommend trying to explain how pathetic it is that a 17 year old seems to have more business sense than him and that he should learn how to properly treat an employee.
As for reasons to not do it, you could attempt to learn from adversity with it and such. That's always a good skill to have. But to be honest, one of my favorite memories from working is telling off one of my bosses when I was 15, telling him what he could do with my job and walking out. It's not often you get a free chance in life to do this without any consequence, I say go for it.
To make this more friendly and PC to avoid a ton of downvotes:
Avoid profanity, insults and the such. Instead, stick to the facts. They will hurt worse anyways. If you want to do it in such a manner here is a decent starting point. This would be in a letter format. I would print 3 copies, one for them, their boss and for yourself.
I am resigning my position effective immediately. I am sorry that it has come to this but I can no longer subject myself to such horrible working conditions. While I am young, I do understand the basic principles of business and management. Treating employees in the manner which you choose to treat employees is not only disrespectful to the employees but it is overall one of the worst possible ways to manage a team.
While I do not want to personally insult you, I feel that you need to be shown the errs in your ways and I truly hope, for your sake, that you can see this and correct this. It will be beneficial for your long-term success hopefully. If you are personally offended, I am sorry.
I believe areas where you can improve are as follows:
Treating your employees with respect.
Recognizing that customer at our establishment do not want a sick employee present.
Continue with areas you think he can improve if any,
I want to thank you for what I have learned during my brief stint at your establishment and I hope that you have learned from myself as well.