Something like "to swell". Some examples:
1. море вспучилось. Imagine whale or submarine floating up from water. Just before they break surface = "море вспучилось". Mass of water rises and "boils".
2. живот пучит = stomach is full of gases. Seethe sounds and pressure make feeling of increasing in size (blow up).
3. пучить глаза = to look at something so intense that "eyes increase in size and move out from orbits".
As far as I see "swollen eyes" in english means state of illnes. "Выпученные глаза" in russian is (3).