Didn’t notify doctor of new insurance by accident. Doctor charged old insurance. What to do?

I started a new job and changed insurance from my parents plan to my own. That took effect on Nov 1, 2022. On December 1st 2022, I had an infusion at my doctors office that I get every 8 weeks. It is expensive (10k -15k range) and requires prior authorization. At my December infusion I didn’t notify my doctor of insurance change because I thought it went into effect at the start of 2023. At my most recent infusion I told them I had an insurance change and they said I need prior authorization on my new insurance. That has now been approved so I’m assuming now I will have to go to my current insurer and notify them the December payment should’ve actually been paid by them. It sounds like there will potentially be a $300 fine. Is there anything else I should do or am I/my parents facing any other penalties for accidentally charging this to their insurance instead of my own?

Note: I was and still am on my parents insurance and I am planning on using it as secondary coverage