I’m being charged $4,000 for my RhoGAM shot

I was sent to the hospital to get my shot by my doctor because of the RhoGam shortage in the U.S. When I checked in to the hospital and gave the prescription I was told to go to emergency and get it there. Just after I got my vitals at emergency they said because I’m over 30 weeks I have to get the shot at L&D emergency so I was taken there. At L&D they drew blood twice and then I had to wait 4 hours before everything was approved and I was able to get my shot. I refused any ultrasound when I was there because I was worried about the bill. I was literally just waiting and took a nap. Now the bill has come and it is for $4,320 after insurance. When I look at the details the shot is fully covered, and the amount is from “observation by hour”. I wasn’t observed, I was just waiting. How can I fight this? do I reach out to my insurance or to the hospital billing department?