This is a new tank, it is bound to go through phases like this. Whenever stuff is growing rapidly in the aquarium, it can distort your test readings. There's no bad stuff in the water, because the growing algae is eating it as fast as it is produced; you're still producing lots of it. You have a higher nutrient load than your system can handle right now, the algae is helping it out.
At one month old tank with fish, either those fish are very new or you did your cycle with fish?
You might have cyano
rather than true algae.
Cyanobacteria, AKA Red Slime Algae
Either way, I would not worry too much about it, just get on a good feeding/maintenance routine and keep it up. If the algae is still there when the tank is 3 months old, then we might look deeper into it.