Tank Disaster

Hey I'm back with another mess :freak:. So I had an eshopps nano skimmer and that broke so, as usual, I put off getting on the phone and calling for another. Now in my tank the nitrates/nitrites/phosphates have gone insane, even with my water changes. The algae has grown so thick that I wipe it off and it comes back the next day to the point that I can't see inside the tank. I have lost numerous corals and it is making me very frustrated. The new pump is on its way, but when it arrives would it be safe to do a 15-20 gallon water change in my tank and a scraping of the algae off the rocks and filling it up with clean new salt water just to get rid of the nasty water? Other than the nitrite/nitrate/phosphate my parameters are in perfect quality and the fish are fine. It is a 29g biocube, 3 years old, lit by kessil