Absolutely, you have spider mites. Also agree try the simple methods first. Even cheaper than Murphy's Oil Soap is 1/2tsp any old dish soap to a quart bottle of water, spray every surface of the plant and soil surface, rinse off after a few minutes. Repeat in 4 or 5 days and again in another 4 or 5 days to get the succeeding generations.
After that, if you can manage to spray down the whole plant once in a while with just water, preferably once a week or so put it in the shower or hose it, that will keep the mites at bay. They like it warm and dry.
Always try the simple, cheap methods first. Expensive, toxic chemicals often aren't any better and are more likely to cause you and your plant harm in the long run. Systemic insecticides become ineffective on Brugs in less than a year, for the exact same reason that antibiotics become ineffective for humans.