Call the medical vendor about the bill. Make sure you write down the names of the person/people who take your call. Explain that you sent payment ages ago, but now see that it was never received. Ask how you can take care of the bill TODAY. Tell them how embarrassing you find it to have any unpaid bills, then very sweetly ask if there's any possible way they could not report this to the credit agencies.
With the cc company, file a dispute online with each of the the credit agencies: Equifax, Transunion, Experian. Just explain that your credit card changed owners, and you were not notified. You took care of payment as soon as you determined the proper owner, and tried to work with the new company about reporting the delinquency. The agencies might not take it off your report, but I believe they can add your explanation to your file, which could help.