The first line of the poem—"I shut my eyes and all the world drops dead"—will be repeated throughout as a refrain. It's an evocative opening, to say the least, as referencing death in the first line of a poem with "Love Song" in the title immediately signals that this won't be a typical ode to a lover.
When the speaker says the rest of the world dies as soon as she shuts her eyes—that is, that everything else ceases to exist—she's immediately suggesting her tenuous hold on reality, the notion that she isn't so sure that anything apart from herself is actually real. This line also conveys the speaker's intense feelings of isolation.
The alliteration and consonance of "drops dead" add drama and weight to this opening image, even evoking the thud of something falling to the ground. The assonance in the long /i/ sounds in "I" and "my eyes" also adds a sense of momentum to the line, these words smoothly flowing into one another as if mimicking the pull of sleepiness or heaviness on the speaker's eyelids. Maybe this signals that the speaker wants to shut out the world, that she views death as a kind of relief because it's too painful to go on existing without her lover.
In the next line, however, the speaker is snapped back to reality: she opens her eyes and "all is born again." The world returns, renews. This doesn't necessarily mean that the speaker is newly optimistic or ready to tackle her pain head-on. Rather, it emphasizes just how wrapped up she is in her own mind: nothing exists to her beyond her own experience. If she can't see "all the world," then it's not there. She can't be sure of anything beyond her own individual perception—and this pushes her to question the reality of the lover who has apparently broken her heart.
Indeed, having opened her eyes, she now wonders if she imagined this vague "you" to whom the poem is addressed. The parentheses enclosing this phrase highlight the intimate nature of this poem, granting the reader a peek into the speaker's mind. In suggesting she “made” this person “up,” she’s questioning whether her perception of this lover and of their interactions lined up with reality. Maybe she only convinced herself that this person loved her or that they had something special; maybe she projected her own fantasies onto this "you" and is now grappling with the truth of the situation.
Though Plath’s poems don’t have to be read exclusively as autobiographical, some context can help orient readers here: Plath wrote “Mad Girl’s Love Song” after being stood up for a date. Rejection is painful, and the speaker’s agony in the poem certainly suggests some deep heartbreak. Knowing the poem is inspired by this event also clarifies why the speaker questions her own perceptions: she thought this person was interested in her but then he failed to turn up when expected. That would likely make anyone wonder whether they’d misinterpreted someone’s intentions!