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The New Testament does not say that the couple should get married. Under the Old Testament law a man who had premarital sex with a woman was obligated to marry her (Exodus 22:16), but we are not under that law (Romans 8:2).
Some teach that sex is the same as marriage in God's eyes. However, Jesus' dealing with the Samaritan woman in John 4:16-18 prove otherwise. She had previously had five husbands, but the man that she was currently involved with was not her husband, and Christ did not indicate that she should marry him.
The bottom line is this - you should only marry the person who the Lord wants you to marry (I Cor. 7:39). Premarital sex is a sin, but the sin should not be compounded by marrying a woman that the Lord does not want you to marry. By illustration: we know that is is a sin for a Christian to marry an unbeliever. Does the fact that a believer had sex with an unbeliever negate the fact that he should not marry her? I don't think so.
You use the word "mess" wisely. Premarital sex always messes up the lives of those involved, and the lives of those with whom they may be involved in the future. This is why Paul says to "Flee fornication" (I Cor. 6:18). However, the past can not be undone; it can only be forgiven. Thus, I believe the guilty parties should confess their sin to each other and to the Lord (assuming that both are believers), and move forward in their Christian lives with a commitment to never repeat that sinful mistake.
Even if a child is conceived, I do not believe that this changes things. The father should make sure that he takes care of the child both financially and in any other way that he can, but this does not mean that he must marry the mother. Unfortunately, there are consequences for the decisions that we make, and "they have sown the wind, and they shall reap the whirlwind" (Hosea 8:7).
I hope this helps. May the Lord bless you.
Pastor Dr. Mark Montgomery
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Ambassador Baptist Church
1926 Babcock Blvd
Pittsburgh, PA 15209