You need to use a filter or you will damage your camera lens. This is why you have the red glow. A full eclipse is the only part you can look without a filter.

I'm not sure how they took their photos, but mine looked the similar since I needed to use a filter when not in the total eclipse

I used a cheap o filter on my lens that was basically a version of the glasses if it was bigger enough to fit the lens. It also didn't help that I didn't have a telephoto lens for this photoshoot to capture more of the detail and I probably didn't white balance correctly.