I am having a cbc & a cmp blood test tomorrow. Will the hydrocodone I took today even show up in that test? This test is to check my Lithium level.

The hydrocodone will only show up if the analyst does the analysis specifically for it or for compounds in that class (i.e. a drug screen). I doubt seriously that they will see it when checking for lithium.

It would show up if they asked for a drug screen to find it.