How do I know if my dentist is trying to get over on me?

I had some cavities to fill after not having insurance for a while. I decided to bite the bullet and go out of pocket. The issue came when I had my second session. I was told I have 6 cavities (all four back molars and two right next to them), when booking my appointments I was told I would first do the left side, then the right side, so we booked two appointments. I was shown only two costs of about 500 then 600 (each has a discount applied to it). Being that it was a month ago that I booked it, I now can’t say for 100% certainty that they said I am booking only one side.

The issue came during my second appointment when I learned they are going in quadrants (upper left, lower left, upper right, lower right) yet I have been paying the full 500 and 600. I know for 100% certainty that this is the first time the word “quadrant” was used, they repeatedly said left and right “side” when booking. Obviously I was expecting to pay a little over $1k, now it is $2k which I can’t afford since I am about to start graduate school. My first and only warning sign was my after first appt when they asked if I would like to book the “side” that they had just worked on. I assumed it was just a receptionist out of the loop and not knowing it was really the other side I have next, so I said I already have that booked. She checked, saw I had it booked and said I was good to go (she never mentioned anything about needing to book any other appointments aside from my next cleaning in 6 months).

I was thinking of requesting a itemized receipt, but I want to be smart about this if there is foul play going on. Should I request the pictures of my teeth first so I can just send it to other dentists for a better price? I feel like if I ask for both it will raise their red flags and make it harder for me. Anything else I should do?