You should go out and buy a test kit, red sea or salifert are what I would use for NO3 readings and a Hanna checker for phosphate. Test kits are important for reef tanks, you’ll need to monitor calcium, magnesium, alkalinity and other things in order to have coral that grows well.
First thing you should do is attack the problem of algae, which is going to be elevated NO3 and PO4. Water changes, a good skimmer and feeding less are good ways to do so. A properly sized cleanup crew will also help, but typically they won’t eat huge chunks. If you trim it down by hand they can help control it well though.