The dictionary says a prom is a
"formal dance given by a high school or college class." 

Dancing is defined as
"to perform a rhythmic and patterned succession of bodily movements 
usually to music, to move up and down or about."

The Bible word which describes and condemns dancing as sensual and sinful is lasciviousness – "unbridled lust, excess, licentiousness, wantonness, outrageousness, shamelessness, insolence, indecent bodily movements, unchaste handling of males and females" (Thayer, p. 79).

Dancing certainly involves "indecent bodily movements" and the "unchaste handling of males and females." That is its design and appeal.

Dancing involves activities that incite lust, passion and eroticism. Regarding such we read, "That whosoever looketh on a woman to lust after her hath committed adultery with her already in his heart" (Matthew 5:28). "Every man is tempted, when he is drawn away of his own lust, and enticed. Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death" (James 1:14,15).

Arthur Murray, a noted dancing teacher, was quoted in Readers Digest as saying: "The difference between wrestling and dancing is that, in wrestling, some holds are barred!"

A former owner of a large dance hall said, "You can picture the effect on a boy or girl...at one of these dances which calls for close abdominal contact and frequently brings the cheeks together and entwines the limb. There is but one reason for its popularity. That reason is sex appeal."

Lasciviousness and wantonness, which describe dancing, are condemned in Mark 7:22; II Corinthians 12:21; Galatians 5:19; Ephesians 4:19; I Peter 4:3; Jude 1:4; II Peter 2:7; Romans 13:13 and II Peter 2:18. 

Those involving themselves in lasciviousness have no hope of heaven 
unless they repent and stop the activity

Scripture says:
"...that they which do such things shall not inherit the kingdom of God"
(Galatians 5:21)