There are two main things that cause a head tilt in rats: inner ear infection and a Pituitary tumor. Either way your rat needs to go to the vets as fast as possible. Head tilts resulting from infection need to be treated immediately and aggressively with antibiotics and steroids (usually prednisone).
I would print this page out about
inner ear infections and the
RMCA drug chart which gives the correct doses of meds for rats and take them both with you to the vets.
In the mean time try to make sure that your rat can't fall off levels in her cage and offer her foods that are easy to eat, stuff that's soft like oatmeal, baby foods etc. Make sure she's drinking enough and she's kept nice and warm. And no more shoulder sitting for the time being!
Beth