I have not practiced singing all that much so I am reluctant to sing but I have found that my spirit is strengthened and encouraged when I sing hymns and I think this is something that God willing I am going to try and make a regular practice (outside of any corporate setting). I believe we all should be signing hymns by ourselves as well and should be supplementing our prayer lives with them. The singing of hymns is something specifically mentioned in addition to spoken prayer as we see when the Lord and his disciples sing a hymn right before they go out to the Mount of Olives on the eve of the Lord’s crucifixion (Matthew 26:30). We also see Paul and Barnabas singing hymns when they were in prison (shortly before being freed) (Acts 16:25). Of course singing is a part of the Old Testament pattern of prayer, as it is not for nothing that many of the prayers of the psaltery are specifically meant for musical accompaniment. There are also priests specifically designated as singers (1 Chronicles 9:33).
So singing in my opinion is a fundamental part of worship, no matter what we think of our voice. It is also worth noting that the Lord and the Apostles both were singing in times of great distress, indicating that the hymns were used to lift their spirits. So especially when we are feeling depressed spiritually we should sing to raise our spirits, but singing should become a part of our regular prayer practice regardless.