Help on posting images on the sidebar (all users)

I’m very new to WordPress, and this is the very first theme I make. I have been experimenting with posting images on the sidebar, and I’ve done it using the text widget and then just adding each image manually there. It works, but it’s probably one of the worst ways of doing it: only the admin can edit this file (I think), it’s not very user friendly and it gets deleted every time I change the theme.

What would be the best way to do it? Ideally, I’d like every user to be able to post images there, just as if they were writing a regular post.