| Leave them bare for now. you're roommate is likely taping her arches because she has Plantar Faciitis or has a history of pain in her arch from running. You don't know if the issue is your lack of impact related activities or a bio mechanical problem.
See if running on the rubberized track or treadmill helps you. Both should provide you with a lesser impact than running on a paved surface. Grass would be the best (assuming you are in a warm climate and the ground is soft)...speaking of which...where are you located?
Also do take Doug's advice about investing in good running shoe's seriously. If you have the ability, go to a running store and get your stride examined to see if you are a pronator, supinator or a neutral step and have them recommend the best shoe options for you with you choosing the ones that feel best. They can also recomend shoes based on your complaint of knee pain, recommending a shoe with a higher shock absorption ability to lessen your impact. | 
