I think millipedes are faster? Who knows.
Anywho, it *looks* like you have a Schefflera. They do okay with pretty good pruning, so I wouldn't worry to much about cutting it back. And it might be a good opportunity for you to practice some plant propagation - especially if you decide the bugs are too much to deal with and you want to trash this one.
Stush's advice is good, but admittedly, I won't use most of the insecticides on the market if I can get away with other means - especially inside my home. Oftentimes soap and water are the basis of good care, unless you get something ugly like mealies or scale - but that's a whole 'nother post.
What *I* would do.... I'd go buy a bag of potting soil. I'd take your plant outside, take a bucket of warm soapy water and wash all the soil off of the roots. This will give you chance to see if there's something eating your roots, as well as (hopefully) taking whatever is in there and putting it outside. Then I'd re-pot the plant in the fresh soil, using a larger pot so it doesn't fall over again!
You also might want to back off of the water a little - that might be where the bugs and the large amount of growth came from.
HTH!
