There are some reasons I can think of, and they are not mutually exclusive if true.
1) There is more moisture in the sky. This enables sunlight to scatter more, and so the sky appears to be brighter.
2) The rain is able to clear dust, pollutants, etc. which normally block sunlight. With less of these particles in the air, more light is able to come through the atmosphere.
3) The wet surfaces present after raining are more reflective, and so more light reaches your eyes.
4) If your eyes were used to the limited light during the rain, then perhaps your eyes are more sensitive to the brightness.
In any case, I don't think this has anything to do with refraction though. If refraction properties did change, this just influences the angle at which the light appears to come from, but this would not influence how much light actually reaches your eyes.