You're not "unlucky", the odds are against you. :P
With Old Rod:
Encounter Chance: 60% Magikarp, 35% Tentacool, 5% Feebas
With Good Rod:
Encounter Chance: 60% Magikarp, 35% Carvanha, 5% Feebas
With Super Rod:
Encounter Chance: 60% Carvanha, 35% Sharpedo, 5% Feebas
No matter what Rod you use, you will have a microscopically low 5% encounter rate for Feebas. You'll have to search a lot to get a Shiny Feebas. If you do use a Super Rod, you can encounter a lot more Carvanha rather than Magikarp.
So, unfortunately, it is very difficult to get Feebas in general. Hope you do get a shiny one someday!
Hope I helped!