I do not think that the USA should be worried. I think that the Korean leader is a publicity monger and drama addict. He really enjoys the publicity that comes with his threats and posturing. As an example, he carried out one of his tests when President Trump was visiting South Korea. He was just making sure that he also made enough noise in order to get some attention.
Despite what he wants the world to believe, North Korea is in a very bad shape economically. There is no way they can start a war with an adversary who is economically and militarily superior to them. A war effort reallytakes a lot out of the resources of a country and currently, it would be better for North Korea to allocate their rather scant resources elsewhere.
Militarily, the logistical arrangements would be a nightmare for North Korea. While America has allies of note close to North Korea, the same cannot be said of North Korea.