A week ago I dyed my natural hair color from a lightish brown to a way darker brown not black, but almost.
I've been rinsing it with baking soda and dandruff shampoo the past two or three days and it's fading a little.

Is there anything I can do to get my natural color back without killing my hair or going to a salon?

If you are not prepared to bleach/remove the colour out then the only thing you can do is by fading it with deep cleansing/claifying shampoos. It will not totally remove the colour either. But it will fade it out quite a lot.

Dying over it will result in funky colors. Your best bet is to strip it and dye over that, but that will ruin your hair, and you should have it professionally done.

So, try Prell to fade it, but be sure that you keep your hair moisturized! Using baking soda or color lightening shampoos really can damage and dry your hair out. With most hair dyes, though, there are really good conditioners that come with the dye. Using this a few times a week will keep your hair healthy, or healthier.