You can buy a potion of Cure Ailment. If you are an Alchemist you can make this potion.
If you are skilled in Divination you can cast a spell to cure it, or at least cast "create food" to keep from starving to death.
If none of these work, then you need to make it to the next biggest town/village to see if they have any of these. Luckily, tapeworms are just about getting hungry quicker- it doesn't alter any other stats. So, make it your priority to get to the next town as quickly as possible.
As for QuickTravel- it's all about getting from city to city as fast as possible. No rest; no time to heal. But you still consume food. Still, it's the fastest way (in terms of game turns) to get between cities.