Either you or your attorney has to appear. If you want the public defender, you must appear at your first court date. You will then be referred to the public defender's office for eligibility.
There will be a second court date and I do not know if the public defender (assuming you are found eligible for their services) will appear on your behalf without you personally present. A private attorney can always appear on misdemeanor matters (except domestic violence, etc.) without you having to personally appear. If you appear the first day by yourself and just "plead guilty," you probably won't have any further court dates, but you would have forfeited any defense or favorable disposition you might have obtained with an attorney.
You need to appear at the first court date to get a public defender or retain an attorney. An attorney can appear on subsequent court dates for you. Hopefully, you will qualify for some alternative sentencing. This usually involves community service and/or a fine.
Relax; more people than you think make this “STUPID MISTAKE!” So, don't be too hard on yourself! You can hire an attorney to go in on your court date and handle the matter without you being present. Actually, you don't have to be present for a majority of the case as you’re being charged with a misdemeanor. You can even plea (if it comes down to it) with a notarized TAHL Waiver.
I suggest that you read my Petty Theft Guide:
Criminal defense Criminal charges Misdemeanor crime Criminal charges for theft Crimes against persons Domestic violence and criminal charges Right to counsel in criminal cases Defenses for criminal charges Criminal sentencing Alternative sentencing for criminal conviction Court-ordered community service for criminal conviction