But when I am in a relationship I don't have a strong desire to have sex or fall in love with others.
Sounds like "monoamorous" in love style preference to me -- the desire or capacity to love one at a time.
And I don't think I could feel comfortable with my partner having sex or falling in love with others. I THINK I could MAYBE handle a once a year exception to the sex thing or something like that. I THINK i could MAYBE handle us having a couple we were friends with but not in love with to mess around with from time to time as long as nobody was being deceptive.
Sounds like not necessarily "exclusively monogamous" in relationship shape preference then. Interested in experimenting with "polysexual" maybe? Not casual swinging sex with acquaintances, but steady FWB?
It's all spectrum. In the end it is up to you
what serves you best at this time or what you want to explore.
I'd like to note though that what serves you best/what you are willing to explore in your 20's, 30's, 40's 50's and so on can all be different.