I don't seem to have been privy to this statement....
I ask because this statement "but running and hiking can make me feel a little bit like I'm dying - lightheadedness, heart working overtime, pins and needles in my limbs. Major postural changes like going from crouching to standing make me dizzy too. I'm fine once they pump me full of the good stuff of course"
If this is the case, then obviously flying at altitude (oxygen desaturation curve and all that), could cause problems.
If your problem relates to the number itself, then this could be less of a problem
You need someone who can sift your symptoms (if you have any), your signs, and a look at your blood work in detail.
Your dose of iron was sub-therapeutic.