Do I really have a doctor?

I'm 30 weeks pregnant, I just moved to another state and my insurance is pending. I went to the human service office where I get WIC and they have a prenatal clinic that I will start going to on Wednesday. But, in my previous state I had insurance and I had an actual doctor. Now, I don't have insurance and I will be attending this extremely busy clinic. Now, I asked a question before about what hospital I should give birth at, and everyone said to ask my doctor which hospital he will deliver me at. But if I'm going to a clinic like this will I even have a doctor? I know a doctor will check me out, etc, but it's not like he's my personal Ob/Gyn. I've never been to a clinic like this before, so I'm so unsure as what I should expect and this is my first baby so I'm even more nervous. I want to deliver at the top of the line hospital that is down the street from me where I can trust that everything will be fine, and not at the clinic's hospital with a doctor I barely know anyway. But will he even deliver me, or will I just be up for grabs for any L&D doctor?