Adam, welcome! Actually, I agree with you, I think this self-portrait came out pretty good considering you were holding the camera out in front of you like that.
On the second shot, a single-light portrait can always be a challenge. I would recommend that you find a second light source: a window, a reflector, something. You just need something to keep the details in the shadows. Good start. Keep 'em coming!
I agree with some of the previous posts. A S/P is tough and focus is the thing that trips up the photog. How can one focus on the model in front when you can't see the focus point?
The second shot seems soft as well. The composition cuts off a portion of her elbow or the clothing in that area. Try to avoid that, but still put her off center as you did.
