Claustrophobic about caves?

My father and I were spending time together and one of the places we went was a cavern. Its called Lost River Cavern at Pennsylvania. At first, I looked through it, and I was unsure. It was said to be 40 minutes long. There were small spaces and after 4 minutes or so, I couldn't go any farther. There was a little kid who didn't worry at all but I had to turn around... I couldn't take my mind off of things happening like "What if it flooded... Or what if something in the rocks made them slip and we were trapped?" I was terrified and my dad payed the money ( 22 dollars ) and i felt like crap :\ anyone know how to stop yourself from thinking about it or getting scared?