Time Travel question

Hey! So I can't get this book that I read a long time ago out of my head and I also can't seem to remember the name or find it anywhere, so any help would be great! Here's what I remember about it:

Girl MC who figures out she can travel between realms by doing this kind of "side step"
People can tell time in this alternate world by how the air smells (don't ask how I remember that strange detail, but I do for some reason)
The girl is some kind of royalty in the other world
Pretty sure she was adopted in our world
Some guy from the alternate world (bad guy) wants to marry her and I think they do get married and during the ceremony there is some kind of wax poured over their joined hands but right when that happens she side steps and tries to loose him somewhere between the worlds
She is either one of the only people or the only person who can travel between the worlds
I'm pretty sure in the beginning of the book she goes to some kind of physics shop or something cause she's trying to figure out what's wrong with her or why she is feeling weird or something

So that is all I can remember at the moment. If you've ever read anything that sounds like that please let me know!! Thanks