I am sorry about your arrest.You state that you can honestly state it was inadvertent.I don't undertsand.In most states, a theft crime is what we lawyers call a specific intent crime.Put simply,it means that you must have mentally intended to commit the crime and then committed it.If by inadvertent you mean for instance that you absent mindedly put an object say into your pocket and walked out of a store,you would not have had the mental state required to be guilty of theft.However,proving to a jury of your peers or to a judge that your inadvertent action was a mistake and not a crime requires an analysis of the specific facts of your case which you have not layed out in your question.
Most petty theft crimes ( I am assuming that the object of the inadvertent shoplift was not of a high value item), can be handled by the public defenders office.I would not go out and hire a private lawyer for such a case.As long as you do not inadvertently commit any acts that could be considered theft in your immediate future,and stay law abiding, you should be able to come out of this a better citizen.Take care of the matter,Don't sweat it.
Although you may have made a serious error of judgment, it is good that you now recognize the seriousness of your situation. Not to make you feel worse, but I routinely advise clients that a conviction for a crime of dishonesty is likely to have more effect on your life than conviction for almost any other type of offense, other than a serious crime of violence (attempted murder, for example) or a sex offense. Even if you have a clean record for 30 years, potential employers will always be thinking that you are a dishonest and sneaky person because of what happened when you were barely out of your teen years.
For that reason, although it is likely that an assistant public defender just like any other attorney could work out a deal that can can keep you out of jail, I think that you probably ought to come clean with your parents, tell them you made a serious mistake in judgment, and that you need their help in obtaining private counsel who has the resources to fight for the best possible disposition. Of course even private counsel cannot guarantee success, but your odds are usually much better just because you will have so much more individual attention than an assistant public defender has the resources to give you.
Please note that if you are charged in D.C., you would likely be represented by private counsel paid under the Criminal Justice Act rather than by an employee of the Office of the Public Defender. CJA attorneys vary greatly in ability, in my experience, from excellent to terrible, and you will normally be stuck with whoever you are assigned.
You probably don't need to panic. If this is the first time that you have committed a criminal offense, the District of Columbia has special programs for first time offenders such as shoplifters, where you can get your case dismissed provided you do not commit another offense during a set time (usually 6 months), and you complete a certain number of community service hours (usually 40 hours) in that time. You would have to come to court at the end of the six months, and the government dismisses the case (enters a nolle prosequi) upon proof shown that you completed your community service. I have handled probably about 70-80 of these types of cases during my time in practice, and provided you follow the requirements, almost all the cases get dismissed without a problem.
If you cannot afford an attorney, the court will appoint one for you. Generally, the court-appointed attorney system is rather good in DC, so you should get someone who is rather experienced in these types of matters. Good luck to you.