I'm really struggling to grasp singing from my diaphragm. Am I screwed?

I took singing lessons for the last 3 months. The lessons were scarce (one hour every two weeks, so two times a month).

Sadly, I really don't feel like it went anywhere. On top of the lessons being scarce, I just don't think the teacher was the one for me for a variety of reasons.

But the thing that's frustrated me most is that I feel like I still haven't grasped "singing from my diaphragm". When I sing to myself (which is often) I feel I sound best when I just sing the way that feels naturally, but I'm not sure doing that is actually singing "from my diaphragm". When I try to make a conscious effort to really sing from my diaphragm I feel like I barely notice a physical difference. My frustrations are compounding and at this point I feel like if I can't grasp this basic I should just stop all together.

Is it possible to sing well without focusing on singing from your diaphragm? Or is there a chance that I actually am singing from there and just not noticing (I don't know if it's super noticeable to the singer or not)?