TIC useless at resolving medical claim

I travelled to New York in September where I fell ill with a chest infection while pregnant so in order to ensure the safety of my unborn child I went in search of medical assistance at the Lenox Hill Hospital because I had travel insurance with TIC. I was treated and then presented with a massive bill in Dollars and after some time we managed to get ahold of TIC customer service and have the matter resolved. It was believed that TIC would handle the matter. Later when we got home, we started receiving emails and post from this hospital requesting payment. After many back and forth we were assured that the matter would be resolved but after a few months we would either receive more emails or more bills in the post. Today, I have received yet another letter of demand from the hospital in question... I will be contacting FNB lawyers now to advise on how to settle the matter as TIC is completely useless and have been from the get go. DO NOT TRUST THIS COMPANY TO SORT YOUR MATTERS OUT. I repeat DO NOT TRUST THIS COMPANY. Stay away, they really are the worst.