Did I really get the job??

I have been applying for jobs with the state of Fl in regards to being a probation officer. Two weeks ago, I signed a conditional offer of employment. When I called to check on the status of my physical and drug screen, I was told there was a hiring freeze. So....I was crushed. Anyways, I decided to try one more avenue....nurse recruiting. I have a little background in that....although it is 75 miles away from me. I went on the interview today and did very very well. The woman who interviewed me kept trying to get her boss to interview me so I wouldn't have to come back for a 2nd interview....long drive. She told me her boss "loved me" and that they definitely wanted me and I would be starting around Dec. 17th and that she just needed to do a background check and verify previous employment. I have gone through this before with the state of Fl and then been disappointed. Should I really think that I have the job? It went so well. Do they usually offer the job on the first interview?

You probably got it, assuming your background check comes back clean. It's not usual to get an offer at the first interview, but it does happen.