Birth control question help me out PLEASE

So, I started this birth control months and months ago but I stopped it because I wanted to switch it and my doctor got it confused and called in the same birth control blah blah blah. I have this left over and I can't call in more because my insurance was canceled. Well since I'm off birth control my acne is horrid so I decided to start it 3 days ago. The first pack of this was gone obviously so this is the 4th day I've been on it. (I haven't taken the 4th pill yet, it's the last pill of the first pack) I'm wondering if it will still help prevent against pregnancy too even though I didn't start taking it correctly. I know it takes 7 days to work (if it even does work) and I'm in no rush to have sex without a condom I'm simply just curious and plus it would make me feel better if I was on birth control.