How does one repent for zina? What if the man is someone who I’m planning to marry anyway since we are close to being engaged? Will the punishment be as severe, especially since we both feel guilt?
If you both truly repent (meaning that you ask for God’s forgiveness and intend to not repeat the sin), then it is the consensus view that the two of you can marry without issue according to a fatwa by the Egyptian scholar Khālid b. al-Munʿim al-Rifāʿī.
Before marrying (before nikāḥ) you must wait one menstrual cycle to ensure that you are not pregnant. If you are, according to the Ḥanafī and Shāfiʿī schools, you two can still marry, while according to the Mālikī and Ḥanbalī schools you cannot marry until you give birth. The Ḥanafī and Shāfiʿī opinions are preferable since this is better for the two of you, the child and for the rest of society (to marry now rather than later if you have became pregnant). If you have your period like normal, then you can marry according to all the schools.
There is no punishment, that is only something relevant if the issue reaches an Islamic court (if people saw you during the act then went on to report on you in a country that follows Islamic law). Since what you mention appears to have been done in private, then it is sufficient for both of you to repent, and that is the end of it. This is the opinion of the Saudi fatwa council.
In short, both of you should repent, then you can marry like normal (taking into account the complications mentioned above) and go on with your lives. Both of you should do extra fasts and worship to prove to yourselves and to God that your repentance is true.