Sounds like popeye - use an antibiotic like Maracyn I or II, Kanaplex, or TriSulfa. Popeye can be an indicator of poor water quality, meaning that there may be some ammonia present. How big is the betta's tank, and how often do you do water changes? Do you have a filter and a heater? Do you test for ammonia and nitrites? These parameters should be 0 in a cycled tank. Sometimes small betta bowls don't cycle, because they are so small, and betta illnesses like popeye or finrot can result.