A speaker is trying to get through an ordinary errand while something terrible weighs on them. The "white noise" in the first lines suggests numbness: the world has gone muffled, and the speaker can't take anything in. Yet life keeps making demands. They still "needed groceries," so they have to go out among other people.
The poem's turn comes in the last lines, where the speaker feels watched. Everyone seems to be looking at them "like it was me that murdered her." We can't tell from the poem whether the speaker is truly suspected, or whether they only feel that way. Either reading works. The speaker could be someone close to the woman who died, imagining blame, or someone actually under suspicion. What comes through is the feeling of being exposed and judged.
The mood is tense and claustrophobic. The short lines at the end drop one word at a time, like slow, heavy steps, and the final word "her" lands with a thud.