This happened to me when I went to buy my house. I had an "outstanding" $48 and $150 in medical bills due. When I paid them, I got checks 8 weeks later for the exact amounts I'd written, stating that it was over-payment. When I called the hospital, they said that collections didn't have updated billing records.
1) Contact the clinic
Ask if you actually owe anything. They'll be able to pull all of the billing records for your account. If you do owe something, let them know that your insurance was supposed to cover that. If they insist that insurance doesn't / didn't, then you're liable for whatever is left. If it has gone to collections, you'll have to pay through the collections company, not directly to the clinic.
2) Contact the collections company
They are notoriously bad at keeping their records up-to-date, and will continue to report "unpaid medical" until you pay it or they clear it. If the clinic says you're paid up, let them know that. They will contact the clinic to get the billing records. Once that's cleared up, move on to...
3) Contact the credit bureaus where this is affecting your history
You can dispute an item to have it removed. They will contact the collections company and raise the dispute. If you've contacted collections, and they know you don't owe anything, they'll clear it when the dispute reaches them.
This process can take a few months to complete (and for the bad mark to be removed from your report). In general, a single $250 medical bill past due doesn't have a huge effect on your credit score, but it's always good to get it cleared up.