Our Prophet Muhammad (salla Allah alayhi wa sallam) said, "Every religion has a special characteristic. And the special characteristic of Islam is modesty (haya)" [Ibn Majah].
And he also said, "Modesty is a branch of faith" [al-Bukhari].
Feeling shy to commit sins, or to expose one's body, or to be known as a bad person, is actually a good thing. "Haya, all of it, is good," and, "Haya does not bring evil" are both famous traditions.
That is why when shyness is removed, it is the final barrier between you and committing evil. As the famous tradition says: "If you have no haya (modesty), then do as you please!" [Tirmidhi], because once modesty and shyness is removed, there is nothing to stop one from publicizing ones sins and boasting about it. Eventually, a stage will be reached where publicizing sins and reveling in disbelief will become a badge of honor for such a person.
It is human to commit sins, and all of us are humans and sinners. But haya should make us embarrassed of our sins in front of our Lord, and ask Him for forgiveness, for He knows all and forgives all to those who ask. And haya should make us conscious of committing sins in front of others, and this aspect of modesty is normal and Islamic.
That is why our Prophet (SAW) said, "Allah shall forgive my Ummah their sins, except those who publicize them" [al-Bukhari]. A repentant sinner is embarrassed of his or her sins, and will ask Allah to forgive, and so shall be forgiven. But the one who sins in public, and publicizes those sins, has demonstrated a complete lack of haya, coupled with the evil sin of arrogance, and hence there is no remorse, and no forgiveness.
May Allah make bless us with haya and faith!