ER + doctor’s billed wrong insurance, I owe something I didn’t know about, need some advice

I currently have Medicaid in New Hampshire. Last year for school, I got a student health plan, Blue Cross Blue Shield of MA. After moving back home, I had to go to the ER and my doctor’s office (both in NH) shortly after. Both times, they asked if the Medicaid plan is still my current plan, and I said yes. I logged onto my BCBS portal earlier since I’m planning on cancelling it, and I noticed that the ER and doctor’s office billed BCBS instead of Medicaid. I didn’t give them the information for that plan, so I’m not sure how they got it. I owe $120 in co-pays, 100 for ER, 20 for doctor’s office (which I wasn’t informed of at the time of the visits), which isn’t a huge deal, but that would put a dent into my savings at the moment (which isn’t a lot).

I called BCBS and they told me to call the hospital and have them bill the correct insurance, but BCBS already paid both claims. I was wondering if this would open up some can of worms I’m not thinking of, since they technically already forked over the money for both visits. If I call the hospital and switch it over, I wouldn’t owe the co-pays, but I don’t want to possibly owe the full amount if something billing related happens since it was already paid by BCBS.

I’m new to health insurance stuff so I apologize if this is ignorant and/or me overthinking, I’m just trying to cover all my bases and learn more about this stuff.