Background check...opinions?

I got offered a position at the hospital in my town. I need and want this job so bad. This is the kind of career I'm looking for. I want to be helping people and it pays so well and has such great benefits. I can't keep living off my part time job. I barely bring home 200 dollars every two weeks. The catch is, the job offer is contingent upon my background of course. In 2011 I was charged with 3rd degree harassment (a simple misdemeanor) for fighting via text message with my ex boyfriend. My background has never stopped me from getting a job before but I'm afraid because it's such a big, popular well known hospital that they'll be more strict when it comes to background. What does everyone else think?? :/

Ps. They are already aware I have this charge. It asked about it on the paper I had to fill out for the background to get sent in and I'm always honest about it. They still offered me the job contingent upon my background check.