Hello!
No, it should not. Hydrocodone can have a side effect to release histamine and increase your tendancy to itch but it would not cause a specific vaginal rash. If an allegic reaction then it would be possible to have a generalized rash all over your body. A focal rash in the vaginal area must be something else going on. I hope this helps. Follow up questions are welcome if you have any.
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Anthony Bray MD
Doctor
14 years as clinician in the field of Family Practice