Does someone have to be grappled to use Litany of Escape, can I use it on my self and are there any other paladin spells that allow teleportation?
"Target one willing creature that is grappled"
Yes, they have to be grappled.
Yes, you could use it on yourself.
Don't think so. Litany of Escape has a somatic component and you can't cast spells with a somatic component while in a grapple. Swift action spells only remove any AoO, they don't remove the need for somatic components.
Grappling or Pinned: The only spells you can cast while grappling or pinned are those without somatic components and whose material components (if any) you have in hand. Even so, you must make a concentration check (DC 10 + the grappler's CMB + the level of the spell you're casting) or lose the spell.