In her poem, Claudia Emerson adopts a persona, a word taken from the Latin word for "mask." The poem is written from a first person point of view—the speaker refers to herself with the pronoun "I"—but we should not assume that the speaker is actually the poet. In general, it can be misleading to think of the speaker of a poem as the poet since a poet may be writing a fiction in order to make a particular point or convey a certain message. If we assume the poet is the speaker, we may misinterpret or overlook something crucial in the poem.
As far as the poem's addressee, it is somewhat less clear. The speaker never directly identifies to whom she is speaking, so it could be anyone. However, we might speculate based on the way she describes herself as a "middle-aged woman who has nothing better / to do than swim laps in the Y's indoor pool / on a late Friday afternoon." This description, to me, makes it seem as though the speaker is addressing other middle-aged women like herself. Something about the lifeguard seems more youthful, perhaps in part because lifeguards are typically young and because of her study of her "split-ends, hangnail, wristwatch." The speaker seems to be making a statement about her own emotional state at this point in her life, versus a younger woman's. This is a statement that might be difficult to understand if one has not experienced it for oneself.