Is there any chance a small part of swallowed swimming cap cause the problem?

Usually not: People all over the world accidentally swallow little bones, fruit seeds, pieces of objects like toys or jewelry every once in a while. Usually nothing happens, as long as the swallowed item is not a magnet, is not a battery, and is not otherwise leaking toxins. A piece of plastic is considered non-toxic because it will come out of the butt pretty much intact, and soon.