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."

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" (Matt. 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" (Jas. 1:14,15).

Any activity, therefore, that promotes lustful or sensual actions and thoughts is sinful. Dancing is such an activity. John the Baptist was beheaded because of a rash vow made by Herod whose passion was aroused by watching a dancing young maiden (Mk. 6:16-29).

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 Mk. 7:22; II Cor. 12:21; Gal. 5:19; Eph. 4:19; I Pet. 4:3; Jude 1:4; II Pet. 2:7; Rom. 13:13 and II Pet. 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" (Gal. 5:21).