It is likely that your cyclamen is suffering from 'powdery mildew' which is a common problem with indoor cyclamen.
Not sure about the brown specks, possibly another form of mold.
After flowering the plants go through a dormant stage and leaves start turning yellow, which some people may mistake as a dying plant, and add to the problem by over watering. with the correct care it should flower again in a few months. Good drainage is essential and the compost should be just dry to the touch, before the next water is given.
Ideal conditions should be cool and humid, a north or east window is normally good, without too much direct sun. Tempreture 68f in the day and about 50f at night but not below 40f.
They don't like water on the leaves and stems. A liquid feed can be given (as directed) every i-2 months when not dormant. Any dead, dying or diseased looking leaves should be removed.
If the powdery mildew persists it may be worth investing in a fungicidal prey.