What you're describing are just feelings, the sense of self-worth. Those are indeed just brain chemistry. What I (and presumably OP) mean by sense of self is the conscious experience of you being a "self" inside your body, separate from the other. This self could still be the same even with a completely different personality and different feelings. Or maybe it wouldn't be. But the point is that we currently know very little about how we get a consciousness or what it's made of. This may change in the future, but until then I can't say we don't have some form of "soul" with any confidence.

As someone with clinical depression my whole life, I can answer this as no, the depression making me feel worthless is not connect in any way to my sense of "self." That's very seperate from any feeling in general, it just "is."

Sometime I get a feeling/swell of "wonderment" in response to my sense of self if I really concentrate on that "sense," but that feeling of wondermemt is just that: a response.

Also, anti depressants don't work the way most people think they do. In the cases of situational depression, they keep a person getting up and out of bed until they naturally start to feel better, in which case the meds are stopped. In cases of clinical depression though, it's more of a life-long medication that gets them out of bed in the morning. It dulls the depression, but it doesn't get rid of it.

All of that is disconnected from one's sense of "self."