What happens when dreams are put on the side? I mean people shift their dreams for multiple reasons, but this isn't a poem about that; rather, harshly, the dream is already deferred, so what happens, "Does it dry up / like a raising in the sun?" Exists but deflated, "Or fester like a sore-- / And the run?" The metaphor with this line goes in different direction. To fester implies to stay in one place and decay, while running means either to let it keep going or to get away. In this case the ambiguous metaphor is searching for something. "Or crust and sugar over -- like a syrupy sweet?" This line has a a sense of cynicism to it with it being "syrupy sweet." But why? Note something that something rough like crust and sugar is the noun, syrupy sweet then is the taste -- kind of like glossing over the bitterness of losing a dream with and implied (simile) taste.
The stand alone couplet has more oomph, "Maybe it just sags / like a heavy heart." A tad sentimental in the list of interesting metaphors and similes to describe dream deferment, but the emotional impact is there.
The last line, "or does it explode?" comes out of left field image wise, but makes sense when connected with the "heart" imagery -- sag or explode -- the explosion being more prominent of when a dream is lost, a slight second of sudden pieces.