Was Jesus handsome according to Psalm 45:2? You are the most handsome of the sons of men; grace is poured upon
  your lips; therefore God has blessed you forever. (Psalm 45:2)  


Is this psalm about the Messiah or about David himself? Can "handsome" mean something else in this context?

Was Jesus handsome according to this psalm?
Psalm 45 is a love song celebrating a royal wedding.  This view is expressed in the New International Version study Bible, the New Living Translation study Bible and the English Standard Version study Bible.  In order to avoid falling into the trap of giving a personal opinion, allow me to quote from the comments in the ESV:

This is a hymn celebrating a royal wedding; as the title says, it is a love song.  It is impossible to be sure for which king in David’s line the song was first composed, but it does not matter... The psalm has sometimes been taken as directly messianic, because Hebrews 1:8-9 cites Psalm 45:6-7, applying the verses to Christ.  The notes below will make clear how the book of Hebrews uses these verses.
45:1 A Song for a King.  Whether these words are to be sung by the congregation or by a choir, they are addressed to the king.  As a psalm, used in Jerusalem, this would refer to a king in David’s line.
45:2-9 You are a King of Beauty, Majesty, and Justice.  These words speak to the king, praising him for his appearance and gracious speech (v.2), military power (v. 3), and commitment to promoting justice for his subjects (v.4-7a).  These words focus the attention of a young king on the ideals he should hold for his reign and character.  These are what leads to God’s blessing for his people’s king, and to the king’s own respected position in the world (v.7b-9).

In other words, the verse you refer to is not a description of Christ Jesus.  It is a hymn which starts of by addressing the king (to verse 9) then the song turns to the bride and her new role as wife to her husband (the king).  Verses 13-15 describe the splendid attire of the bride (the princess) as she leaves her chamber and is led to the king accompanied by a procession of virgin companions.
It’s a song to be sung at a royal wedding.  The final verses return to the king and speak of the enduring Davidic line.  Is verse 2 saying Jesus was handsome?  No, it is not.  Neither does it mention David.  It seems to be a song to be sung at the wedding of any king from the line of David.
It is true that Hebrews 1:8-9 quotes from Psalm 45:6-7 and applies it to the Son of God, but it does not apply verse 2.
Isaiah 53:2, speaking of the Messiah, says this:

He had no beauty or majesty to attract us to him, nothing in his appearance that we should desire him.&quot;

Physical appearance is of no consequence.