What to do about a woman that we are mutually attracted to in an impossible way to act out now breaks out in hives when we meet in professional situations.

What to do about a woman in a professional setting where acting on desires would be taboo breaking out in hives when we meet to discuss business. There is no prompting from me.

You are the one getting hives?

I suspect that you are sweating around her, and that can bring on hives. But other factors may be present that you can avoid: foods such as nuts, chocolate, fish, tomatoes, eggs, fresh berries, and milk. Fresh foods cause hives more often than cooked foods. Certain food additives and preservatives may also be to blame.
Drugs that can cause hives include aspirin, ibuprofen, high blood pressure drugs (ACE inhibitors), and codeine.

Take an anti-histamine such as Benedryl, and take it on a regular basis as a preventative. Wear loose fitting cotton clothing, and apply a cool damp cloth to your skin if you can.