Brief Answer:
if contain biotin, may have an effect
Detailed Answer:
HI, thanks for using healthcare magic
According to research, the half life of zinc is very very long approx 9 mths. The half life is the time it takes the amount of substance to decrease by half in the body.
This means that the levels of zinc do not alter rapidly so its level would not be affected by your short term use of the zinc supplement to help with your cold.
The other tests would not be not be affected.
If the supplement contains biotin, it is possible that this may have an effect because this distorts some lab tests,this should be checked. If this was not present, then you can have your tests done at any time
I hope this helps, feel free to ask any other questions