Now that I mention it, the brown spot on the plastic canvas that I wiped off just 2 days ago is already back. I'm worried that this algae could overtake my tank? Note that there is no direct sunlight on the tank.
Is there any algae control chemical to put in the tank?
It happens with new tanks. There's not much to be done but wait it out. Algae removers won't do anything because diatoms are little skeletons and not a true algae. Reduce the amount of time your light is on and do a couple of daily 25% water changes to reduce nitrates. If you're not already, continue a weekly 25% water change to keep the nitrates down.