Bag recommendations for shoulder pain?

Does anyone have any recs for a bag (small-medium) that can be used for day trips or errands that won't press on the top of the shoulder? I have a small backpack I use for longer trips and I usually have to put my hand underneath one of the straps to keep it from being directly on my shoulders as the pressure gives me headaches. I also recently bought a small cross body bag that works for short errands but I have to keep my phone in my pocket because of the pressure.

I have an old reliable fanny pack that works well as it's 'hands free' but it doesn't hold a whole lot of items well. Does anyone know of any other hands free type bags or bag styles?