Air carrier First Officer reported a fume event during preflight when the APU bleed was on; resulting in physiological symptoms.

Narrative

When the Captain turned on the APU bleed during preflight; I immediately notice a stinky sock; oil smell. The aircraft had been written up for it 3 days prior. It was very mild; but when I mentioned it to the Captain he didn't smell it. It got slightly worse as we closed the door...I mentioned my concern again; but I was the only one who smelled it. The smell dissipated once we had the engines started; and APU was turned off. I felt like I still could faintly smell it throughout the flight; but couldn't confirm it. After landing in ZZZ1; at the gate we turned the APU bleed back on. This time the smell was undeniable. I left to use the restroom; and when I came back into the flight deck the smell was overpowering; and I now could also feel it in my eyes. I left the aircraft immediately. I notified the outbound crew; at which point they also verified the smell after walking down to check for themselves.I think the aircraft should have been inspected in ZZZ.Fume events continue. It's critical for our health and the health of our passengers to find the source of why this continues to happen. Crews need to be fully empowered to make good decisions regarding fume events to help protect each other.