OT events seemingly alluded to in this psalm.
55:9 seems to allude to the tower of Babel in Genesis 11:1-9.
55:9-11 The picture of the wickedness of the city is quite a contrast with Psalms. 46 and 48.
55:15 "Let them go down alive into Sheol" Numbers 16:30-33

NT and Psalm 55
55:22 Casting our care upon God is encouraged in I Peter 5:7.
55:23 God hurling the wicked to destruction is in Revelation 19:20-21 among other places.  

Jesus fulfills Psalm 55
55:2, 4 The word used in the main ancient Greek translation of the Old Testament translated "anguish" in vs. 4 is a word that is used to describe the feelings of Jesus in John 12:27; 13:21.
55:6-7 Jesus wishes He could flee from HIs burden- Luke 12:49-50.
55:12-14, 20-21 Jesus was betrayed by one who was close to Him- Psalm 41:9; John 13:18