Years ago I hiked to Camp Muir (10,000 Ft) on Mount Rainier and, during the last 1,000 feet of elevation gain, I couldn't catch my breath, I got light headed and when I finally got there I had a wicked headache.
Later my friend made it to ~13,500 feet and he just couldn't continue. He was light headed and couldn't catch his breath. He wasn't able to summit.
In each case we both blamed altitude. Also afterward we each went home, lost fifty pounds, got born again hard, came back and sent the 14,000+ ft. peak in style, joking and laughing the entire way.
I'm not saying that altitude sickness (AMS) isn't real. It kills people all the time. It is nothing to mess with and has nothing to do with fitness or gender. Some people can die going from sea level to as little as 8,000 feet. Their brains swell, their lungs fill with fluid, and now they don't pay taxes.
I'm just suggesting that, if you felt like you were going to die on that 6,000 or 10,000 foot climb you might not want to sell your ice axe and take up croquet just yet. Hit the road, put the fork down and try it again in your new and improved body. You can do it! Probably.