Shoplifting is a crime, at the lowest level an misdemeanor you can spend a nine months in jail over. It's not some traffic ticket that you have the option to pay the ticket and go on, you must appear in court.
Your story is not convincing. The fact that you claim you intended to go back and pay after you had regrets over stealing won't fly anyhow. Once you've concealed the items with the intent of depriving the store of them you've committed the crime and it isn't necessarily reversible.
You should contact an attorney. He can see if there is any defense you might mount. He can also help you possibly get into a diversion program that would keep you from acquiring a criminal record over this. The chances of convincing a judge with your sob story is minimal and frankly, you'd probably not even get to make the case. This isn't like getting sent to the principal's office. You are allowed to cross-examine the prosecution witnesses or introduce your own witnesses and evidence, but it's not a cry in front of the judge because you were wronged situation.
Arrests and charges are public knowledge. If your local paper prints such things routinely, there's nothing you can do to stop it.
Note you can also expect, independent of your criminal problems, to get a letter from the store's "lawyers" demanding restitution for the damages you caused them.

