I'm no expert in Shakespeare's sonnets, but I'll do my best to help out here. I think that you're right. Let's go with metaphor. (Periphrasis might be another option, if that's a familiar term for you.)
Sonnet 109 seems to be a sort of apology for "straying," for being unfaithful to a partner while the speaker was away. (The partner, as you may already know, is a younger man, and this sonnet and others raise some hotly-contested possibilities about Shakespeare's sexual orientations.)
One of the main things that connect this poem to the other poems in this grouping is the emphasis on transgression. The source below includes the following statement:
The theme continues throughout Sonnets 111-120, and the poet uses many terms for the same crime: "stain", "frailties" (109); "offences" (110); "harmful deeds", "infection" (111); "shames" (112); "diseased" (118); "transgression" (120); etc.
The non-literal terms for "transgressoin" here make me suspect that we'll find a number of metaphors in Sonnet 109, too.
I see a metaphor in line 2: "my flame" probably means something like "my intense love." Lines 8 and 11 have "my stain," which probably refers to the infidelity, and "stain'd." Finally, the poem ends with "my rose," which must stand for the loved one.
You'll often find more than one poetic element or device in a single poem, of course. Maybe another poster will have more to say than "metaphor."