Trouble is not an adjective (it can be "troublesome" which means the person cusses trouble.) Bothersome means the person is bothering you directly. A person can be annoying without doing anything to you. The. Meanings are very close! "Bees are bothersome" "That noise is annoying" "We are going to get in trouble if we keep being bothersome to mom. " - "she thinks we are annoying..."