Respectfully, you apply for the services of a public defender if you cannot afford a lawyer. There are financial considerations that determine who is eligible to receive these services. Contact the Court before your Court date, ask for the form to apply for a public defender, and see if you are eligible. If not, you need to at least consult with a lawyer admitted to practice law in FL before you go to Court to understand both the procedures you will be going through; and, the possible resolutions you may have to decide between. Be careful to understand both the direct consequences (like a fine or jail) and the collateral consequences (like how long this will stay on your record). Good luck.
This response does not constitute legal advice. Given the nature of this website, it does not create an attorney-client relationship. This answer is provided solely for informational purposes, for you to use as a starting point when speaking directly with a lawyer in your State. I urge you to immediately contact an experienced criminal defense lawyer admitted to practice law in your State before you make any decisions about this case.
as you are 16(a juvenile) and your offense a minor theft(not a serious person crime), i believe that you are likely going to be dealt with in juvenile court, not adult court. you may be assigned a juvenile counselor(the names vary region to region from counselor, probation officer, caseworker), you may well receive correspondence from that counselor before, or instead of, going to court. that initial involvement with a juvenile department usually involves your parent(s) since you are a minor. depending on YOU, your attitude(willingness to take responsibility for your actions), the juvenile department, district attorney, and court philosophy, their resources, you may-or may NOT-be offered outcomes that do not involve going to court. for example, your case might be diverted into a contract between you, your parents, and the juvenile department, wherein you agree to do, and to not do, certain things(agree to make restitution, do community service, attend certain classes, write apology letters, etc) in a certain time period, and when the contract is successfully completed the matter is closed. even if no alternative disposition is offered, that juvenile counselor/probation officer is likely to prepare you in some manner for going to court. if you lack adequate financial resources, and the consequences of being found guilty are also of a certain kind(incarceration,physical labor for example) you should be assigned counsel to assist you.
I suspect you would be offered a diversion program if this is your first time. A private attorney would be able to negotiate with the State to work out a way for you to complete your diversion requirements in North Carolina.
However, if your parents can not afford an attorney, I would suggest attending your first scheduled court date. Your parents might be able to inquire about diversion then and if offered coordinate with the diversion program about how you can complete the program even though you are moving to North Carolina.