I was reminded of a story when....

.... I was reading ' Shit Happens, But So Do Miracles! by Tanya Allan ' as there are some similarities.

It begins at a boarding school for boys in the UK, the main character goes to bed feeling ill, and wakes up the next morning female.
S/He enlists best friend at the school to help with escape, the runs away to Glasgow or Edinburgh, I think parents wouldn't accept change or might be that character believes this to be the case.
If I'm not mixing stories up while in NYC She meets a shy guy they take a trip through Central Park in horse drawn carriage.
He moves to UK and becomes a teacher of either Literature or Art (I think, definitely a teacher), at Her school.