Spider Mites?

So they're no "furry guy" but I think one of my tomato plants has spider mites. I had noticed a very fine web with tiny white specks around some of the leaves and does it with soapy water. Apparently, these guys love soapy water because they had basically taken over the plant when I checked after a few days.

How on earth did my indoor tomato plant get spider mites? So far I've had red, green, and black aphids, spider mites, those caterpillars that ate my parsley, a deranged bee, and I keep finding peanut shells in my plants. Its had being a plant on the 4th story in Brooklyn.

On a side note, this week's haul: 4 tomatoes, 2 eggplants, 1 green pepper, 2 hot peppers, some basil, and I'll undoubtedly pull in some mint tomorrow night.