Kimmy, thanks for the report. Too bad about the dizziness. Hiking poles can help that, in case you weren't using any.
Since you started feeling it already at 10k elevation, it's a good idea next time to spend 2 days and nights at least at 8k -- Whitney Portal or Mammoth both work. Even better, resting and sleeping overnight at Horseshoe Meadows, at 10k, will put you ahead, as long as just being there doesn't give you the dizziness.
Your unfamiliarity with the trail may have added to your uncertainty. Next time you go, you will notice how much better that part seems.
Start planning your next trip -- I am sure you will have better success next time. ...and the mountain will always be there.
