Sounds like a spider mite infestation. Washing your plant well, especially the undersides of the foliage with isopropol alcohol diluted in water with a few drops of liquid soap added should get rid of them. I'd also mist your plant with water fairly often as spider mites thrive in dry conditions. Another washing with the diluted alcohol might be necessary a couple more times about a week apart. You can also use an insectide/miticide if you choose. Check any nearby plants as the spider mites spread from plant to plant.