Strahad describes jealousy without ever naming it outright, until the final line gives it away: the "green eyed monster." The speaker pictures it as a creature with no body, only sickly green eyes, a color tied to illness and decay rather than anything beautiful. It isn't rage or sorrow. It brings a pain that isn't physical and a longing that isn't for love, and it can't be reasoned with.
The feeling is aimed at someone the speaker clearly cares about. Even happy thoughts and sweet dreams of "you" get tainted. The speaker is caught in a painful bind: the only escape they can see is losing that person, and the fear of that loss keeps feeding the monster. So the jealousy grows instead of fading.
The mood is heavy, tense and unsettled, but not hopeless. The speaker insists the monster "will not break me," and the plain, confessional tone makes the struggle feel honest and raw.