Lily of the Valley by Megan Derr

Lily is the first crown princess her kingdom has ever had, and many look forward to having a queen on the throne someday. Others are vehemently against it, and the anger stirred up by dramatic and severe changes to certain laws is causing even more turmoil.
When that tension finally explodes, Lily finds herself running for her life, forced to leave behind everything she knows and plunge blindly into the dense, dangerous forest that surrounds the royal palace. A forest said to be filled with ancient ruins, monsters, and ghosts who laugh at unwary travelers.
Instead of finding monsters and ghosts, Lily is found by a woodcutter, gruff and quiet and clearly not pleased to be saddled with an uninvited guest who doesn’t even know how to fetch water from a well. But Lily has nowhere else to go, and no way of getting home safely, not when there are people still looking to remove her head.
If she hopes to live long enough to claim her throne, she must first prove her worth to the woman who can’t wait to be rid of her.