Hi mocha delight and Tayla,
It's a good question to ask as there are many alternative strategies to combating depression and anxiety. I always suggest and recommend the ones that have the most evidence behind them which includes exercise, mindfulness and Cognitive Beahviour Therapy and medications (as you have already mentioned). However, there are many other alternative ways to support the treatment of depression. I have included a couple of links from the Black Dog and Beyond Blue which describes quite a few. In my experience, each person is individual from the type of exercise that works (some people feel better doing yoga and others by doing CrossFit) to the dosage and type of medication to what therapist works for you. We are all so unique on our biochemistry, our support structures that what works for one person may not for another.
My recommendation is to always talk with your treating health professional whether this be your psychologist or GP, about trying a new alternative type of treatment.
Here are the links and some of the self help and alternative therapies are listed in both of these sites:
(go to the Beyond Blue link and at the bottom of the page, you can download the comprehensive booklet "A guide on what works for depression - An evidenced based review"
Both of these resources go over the main treatments for depression but also give descriptions of some of the alternative therapies and self help strategies. I hope this helps you on your quest for more knowledge on your healing journey.