People are allowed to avoid any confessor for any personal reason—including the embarrassment over a particular sin. No one is obliged to confess face to face. One is free to go to any parish he chooses for confession.
If one deliberately chooses to withhold a mortal sin in confession, that in itself is a further mortal sin and the whole confession is invalid. If the Lord could suffer such agony on Good Friday to forgive our sins, the least we can do is humbly and honestly confess them. If one forgets to confess a mortal sin, that sin is still forgiven in confession, but the person is required to mention it the next time he goes to confession as an act of sorrow and contrition. It’s the least we can do in the face of God’s love for us.