Um, why is it essential that they DON'T do anything? What does it matter? You don't even have to mention it one way or the other. You can let readers assume things, as long as you show somehow else that they're romantically involved, which you planned to do anyway. In the Egyptian by Mika Waltari, the MC (in the Ancient world) rescues a slave girl and vows to return her to her native native land Crete where she is to be presented as a virgin to the Gods at her temple. MC and virgin fall in love. When the journey is near done, the girl offers herself to MC, is willing to throw away everything so she can be with him. The MC, knowing how important this is to her, declines, and takes her back home so she can perform her rite. At the last minute he changes his mind and goes to the temple to find her, but not before the priest slits her throat and throws her into the sea as a sacrifice. If your chastity vow is anything less interesting that, don't waste anyone's time by writing it.
How is this 'different'? I thought it's pretty common to write more or less starcrossed lovers who due to circumstances can't or won't consummate their relationship. This is pretty much what T and I are doing with our WIP too, plus the girl's a bit choosy and won't spread 'em to just any dick passing by. That kind of stuff can be really fun to read 'cause you keep wondering when will the tension be released? At which point will they be unable to keep their hands off each other? What will be the repercussions if they do do it? And so on. Go ahead, have fun writing
IDK if this will be helpful, but I figured as someone who is in the relationship you're describing, you might like some of my input. My boyfriend and I are both in college, and while we may not be in a war torn fantasy realm, having a child right now would destroy our lives, and we know that it is just something that we are not ready for. On top of that, we are both religious (which obviously adds to the whole 'no sex' thing), but I am the only one of us that is still a virgin. He had many sexual experience in high school, and I am one of the first relationships he has had that lacks a sexual element (that being any act with the word sex attached to it; oral, anal, ect.). For him this has been a really healing relationship, and it has allowed him to feel freer and safer than he has in other relationships. (Now guys reading this, I am fully aware of how hard that is on him and don't think I'm some crazy prude.) I also have been extremely thankful for how slow he has taken things since our relationship has started. Also, just from an economic stand point, the non-sexual part of a relationship is what sells. People say that sex sells, but in reality, it is the build to the sex that sells. Think about it, people rarely watch a show after the two passionate lovers get together. The non-sexual part of the relationship shows the true colors of the people participating. Hope my insight was helpful in some way. If you have any questions, feel free to message me.