You can go swimming. Floating and cooling down isn't going to hurt you. I would check with your doctor if you want to go in the ocean or do the breast stroke.
Sorry about your neck but idk and I wouldn't be able to help you
I had bone spurs removed & pinched nerve openings made larger. It has been 15 years since my surgery & I only wore a soft cervical collar. So I didn't where it during shower, but it was winter. I would think wading or floating would be ok. But swim strokes might be too much.
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