A $100 Pulse oximeter (measures oxygen saturation and pulse) could come in handy to give you a quantitative correlation to your "sick" feeling.
Late last June was the first time I was attempting Mt.Whitney. I drove from San Diego, checked out overnight permit, and camped at Outpost camp the same night. Although in the past I have driven from San Diego and hiked to 11500ft (San Gorgonio summit) and back in a single day, this was the first time I was camping overnight above 10000ft. I had carried a Pulse Oximeter with me. If I did experience any sickness, I wanted to quantify it. That night I had a restless sleep. I could totally feel my pulse pushing my sleeping bag up and down.
Next morning when I woke up (after whatever sleep I got), I felt sick and uneasy. My pulse oximeter read a resting HR of over 100 and oxygen saturation at 85%. I thought this was the time to test my DIAMOX and swallowed one pill. I packed my backpack, and proceeded towards Trail Camp. It was a very slow go, but sometime after I crossed Mirror lake (maybe an hour or so later) I started getting better. Day 2, I setup camp at Trail Camp. Second night I had a disturbed sleep for a different reason. I was peeing every hour or so (This should have been a result of Diamox I guess). I didn't attempt summit the next morning because I didn't have the right gear to scale the chute. But I didn't have the sick feeling anymore. My oxygen reading now was 99% and HR was under 70. Right in time to enjoy the alpenglow of the morning sun on Sierra Crest.