My fiancé and I showed up our private body parts to each other via video calling. We are getting married in a few months. Is this a forbidden sin?
All sin is forbidden. What you were doing involves the sin of lust.
Just because something is done willingly or by consent, it doesn't mean it is necessarily right. "My son, if sinners entice you, do not consent" (Proverbs 1:10). Willingness to sin is still sin. So we have to look elsewhere for the answer.
Nor is the intent that you will marry soon an excuse to sin. The fact is that the two of you are not married.
Being seen naked in front of others ought to trigger a sense of shame. "Your nakedness shall be uncovered, yes, your shame will be seen" (Isaiah 47:3). One of the complaints God had against ancient Israel was the fact that they lost their sense of shame. ""Were they ashamed when they had committed abomination? No! They were not at all ashamed; nor did they know how to blush. Therefore they shall fall among those who fall; at the time I punish them, they shall be cast down," says the LORD" (Jeremiah 6:15; see also Jeremiah 8:12).
The reason is that nakedness is associated with sex. The reason you are showing each other your naked bodies is to stir up lust. However, it is not right for you to be thinking about each in a sexual way at this point. "I charge you, O daughters of Jerusalem, by the gazelles or by the does of the field, do not stir up nor awaken love until it pleases" (Song of Solomon 2:7). You are not married yet. "Let us walk properly, as in the day, not in revelry and drunkenness, not in lewdness and lust, not in strife and envy. But put on the Lord Jesus Christ, and make no provision for the flesh, to fulfill its lusts" (Romans 13:13-14). Lust is strongly desiring something that is wrong to the point of justifying doing the sin in your mind. It is wrong to have sex when you are not married; therefore, it is also wrong to dwell on doing it. "But fornication and all uncleanness or covetousness, let it not even be named among you, as is fitting for saints; neither filthiness, nor foolish talking, nor coarse jesting, which are not fitting, but rather giving of thanks. For this you know, that no fornicator, unclean person, nor covetous man, who is an idolater, has any inheritance in the kingdom of Christ and God. Let no one deceive you with empty words, for because of these things the wrath of God comes upon the sons of disobedience. Therefore do not be partakers with them" (Ephesians 5:3-7).
Sexting is little more than homemade pornography. It is still pornography and it is still wrong. "For this is the will of God, your sanctification: that you should abstain from sexual immorality; that each of you should know how to possess his own vessel in sanctification and honor, not in passion of lust, like the Gentiles who do not know God" (I Thessalonians 4:3-5).