Definitely need to see a nitrate and phosphate test result. How often have you been doing water changes and what is your source water? If you're using tapwater, that could be a big part of the problem. There must be an abundance of nutrients in your tank to be fueling such an algae bloom. Water changes with RO
water are in order.
Also, make sure you have good flow throughout your tank, algae will often grow in low flow areas. If you don't have any powerheads, now would be a good time to add them. Look into the Maxi-Jet 1200, they're powerful and relatively cheap.
I'm also seeing that your tank is only 2 months old. Although not uncommon for new tanks to go through stages of algae blooms, it sounds like yours is to the extreme.
From your description, it sounds like you may have a CPR Bakpak skimmer. The cup you empty is from the skimmer and the other side contains bio media for biofiltration.
For now do a big water change and get the green water under control. HTH