Allergies are a much ampler topic than can be solved by "no drinking red".
Two remarks though:
- no sulphites, no wine. If you're allergic to (even small amounts of) sulphites, don't drink wine.
- test the grapes.
Just "allergic to red" is in many case not a definition.
My wife gets swollen eyes and rash from syrah/shiraz.
No problems with cabernet or pinot noir (although many people don't support burgundy, and that's not a political nor a budgetary remark) and she deals flawlessly with all the whites we know of.