This song uses GOT to express possession.
Got a picture of you beside me = I have a photograph of you beside me.

Pronunciation tips:
T + Y = /ch/ Got your ( "gocho")
vowel + T + vowel = quick D Got a ("godda")

I guess now it's time for me to give up
I feel it's time
Got a picture of you beside me
Got your lipstick mark still on your coffee cup
Got a fist of pure emotion
Got a head of shattered dreams
Gotta leave it, gotta leave it all behind now
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