Hi Mickey,
It would be safer to take the hydrocodone than to use Ibuprophen. None of the prescibed meds will counteract each other. Ibuprophen and others in the same class have been known to decrease renal (kidney) clearances, meaning the body can't flush out lithium at normal rate. This can lead to an increase in blood/Lithium, sometimes to toxic levels. So, as you say the Ibuprofen isn't effective enough for you, better to stay with the hydrocodone.
I agree with what you've said, if it's after operations, possibly the anesthetics temporarily upset your metabolism, not in a toxic sense but enough to effect your well being.
good luck
Nick