SSRIs are good antidepressants overall, clean in the sense that they mostly have one main action (SRI), prohibiting serotonin from being taken out of the synapse. Then the body attempts to retain homeostasis by reducing serotonin release. This leads to transcription factors activating and changing the nature of the cell for the better.
It's a bit strange to me that you're on two powerful antispychotics, but it's nothing outrageous. But SSRIs usually reduce anxiety, too, so maybe you won't need the both of them. Your doctor knows much more than I, but it's decent to talk about with them.
Seroquel is indicated for bipolar depression. Abilify, too, I thought. These are antipsychotics, though, and while two is sometimes done, three seems absurd to me.
Then you have effexor, pristiq, and cymbalta, which are more stimulating, but also have SRI as an action.
Wellbutrin is a stimulating one, too, but isn't an SRI.
Then there is remeron and trazodone, atypical antidepressants.
I mean it comes down to how your depression manifests, which can vary a lot...but in general, SSRIs are a good first defense. They might get a bad rep in places, but they are legit.