They are not granted often, but this is a low level crime, so granting it would not be as risky for the governor as for some others.
You would, of course, have to wait until you complete your entire sentence before you could apply for a pardon. But you could do this yourself without a lawyer and reapply later if it's not granted.
The other option I mentioned is a dismissal in the interest of justice. This would require an attorney and is, like all post conviction remedies, a long shot. But with a compelling reason, a judge has the power to dismiss a conviction, even when there's no basis in law. Although judges do not like doing this, they have in order to avoid an injustice.
You would need to talk to a local criminal trial lawyer to see whether this is a viable possibility for you. The DA would weigh in on this, and they would be very likely to object. So this is not something you can do without a lawyer. But again, once the conviction has been dismissed, you should be able to expunge it from your record.