This psalm is quoted or echoed repeatedly in the New Testament and applied to the suffering of Christ. 

There is no clear record of pre-New Testament sources applying this to the sufferings of the Messiah. 

Psalm 22:1 is quoted in Matthew 27:46; Mark 15:34 

Psalm 22:7-8 is alluded to in Matthew 27:39; Mark 15:29; Luke 23:34-35

Psalm 22:18 is quoted and applied to Christ's suffering in John 19:23-24

Psalm 22:22 is quoted and applied to Jesus in Hebrews 2:12

Does this psalm speak exclusively of Jesus? David was a prophet and is he hear simply prophesying of the experiences of the Christ?
Does Psalm 22 have some reference to David's experiences which are fulfilled in a greater and richer way in Jesus. 
I seek to suggest in this podcast that while these words are David describing his experiences that God selected the words so that he also prophesies about the death and resurrection of Jesus.