There are relatively easy but messy ways to clean them (that may work). First of all, your printer is probably under warranty from Epson, if it was me I would contact them & send it in. I spent forever trying to clean a printhead once, they cleared it right up.
The way to clean it is to take the black cartridge out, put windex or fantastic in the ink inlet (use some kind of tubing), let it sit for a while, blot out with paper towels, repeat with rubbing alcohol to clean out clean, reinsert ink cartridge. You will probably have to repeat this several cycles at least and will end up with black permanent ink on your hands unless exceeding careful.
When you get it fixed, try to print at least once per week to keep the heads clean.