How should I go about handling my depression if I don't want to take medications?

Therapy/self-care. As dr. Krenn said, therapy will help -- ask your primary care doctor or call your insurance about a mental health provider. Things that you can do on your own -- try to establish routines, sleep hygiene, small achievable goals, look for positive aspects of the environment -- do a summary at the end of the day -- best thing that happened, the things i laughed at, etc. To bring you a sense of joy.
Therapy. Counseling or therapy is another option for treating depression. It can be effective in treating depression either alone or in conjunction with medication.