Earlier this week I stayed in a hotel, and within a day noticed bed bug bites all over me. So we decided to check out early and come home. At the time I had no idea what a serious problem they could be and that they could follow us home and become an infestation, but if I had I would have insisted on further compansation. So before bringing anything inside I did some research and my clothes have been bagged outside and I am about to wash them in the hottest water possible but I was writing on some paper and one fell onto it. I killed it of course but now I am seriously worried that that wasn't the only one that snuck in. My skin is highly irritated by the bites and I am paranoid about my new house becoming infested. I was wondering is there something I could make the hotel do or sue them should I have continuing problems, such as infestation to the point of having to replace furniture (of which is a $1500 king size bed less than a year old) , etc. And should I be this worried??

Get a professional involved now, because they can provide you with documentation. What the hotel will pay for depends on the hotel (and their lawyers), but make certain you don't allow a problem to get worse.