You can say "I didn't fake it" or "I wasn't faking it", both are correct.
For my English ears "I wasn't faking it" sounds more accurate because we are talking about a thing that lasts a long time (depression). It is not something that happens in a second. If I wanted to tell someone that I wasn't able to hit a baseball with a bat I would say "I didn't hit it", I wouldn't say "I wasn't hitting it". I don't know how a professional teacher would explain it, but that is how I see it.