The overall conceit this sonnet is established by Shakespeare's allusion to classical Greek mythology, in this case, to Cupid, the God of Love, and to Diana, Goddess of the Hunt, and her handmaiden.
In the sonnets first eight lines, Cupid, asleep, has an arrow stolen by one of Diana's maids, who dips the arrow in a cold stream, which has the effect of heating up the "cold valley-fountain of that ground" because the arrow is infused with Cupid's "holy fire of love." The resulting heat, which is tolerable, proves to provide "a sovereign cure" against a myriad of illnesses.
In lines nine through twelve, the poet tells us that he is "sick withal" and a "sad distempered guest," which echoes the earlier mention of the fountain heated with Cupid's arrow that will cure "strange maladies," which, in the poet's case, is love sickness. Cupid, in order to help the sick poet, needs to renew the arrow's heat by having the poet's love interest look upon the arrow, and then use the renewed love-heat to touch the poet's breast.
The poet, believing that his cure lies in the fountain, still moves toward the fountain, discovering that the fountain provides "no cure," but notes that his salvation comes from the same place Cupid renewed his fire--"my mistresses eyes."
The source of love, then, is not Cupid or Cupid's arrow but the fountain of love, which cures the poet's illness, is the love streaming from the lady's eyes.