Definitely tell your professor! This isn't the first time they'll have dealt with a student with depression. The worst they'll do is say no. Have you gone to counseling? Some things that help me get through a bad depression phase are spending time with an animal, having a plant (incentive to do something productive aka water it, and a sense of accomplishment seeing it grow and thrive, purifies the air, and is related to nature), and changing up my room, even if it's printing out a picture and sticking it to the wall.