Wheat/gluten-free Duluth brews?

If your allergy is specifically to wheat and you're not celiac/gluten-intolerant, you might be okay with several styles, since wheat is more of an adjunct ingredient in beer and not essential to a lot of recipes.  On that note, definitely stay away from "weiss" style beers.  Bottom line is you'd probably need to ask, though (both your doctor and the brewery).  My knowledge is only based on a small homebrewing hobby and I cold be overlooking something.  Unless you're talking to the brewers themselves, servers' knowledge of ingredients can be mixed.

Water.

If you've seen photos of me and my enormous gut you would understand that I am lover of the beer.  I partake in plenty of local and non-local brews and have dabbled in home brewing.  I brewed a nice batch of gluten-free from stuff I purchased at Last Chance last fall and it was pretty good stuff.  So my advice: Look into home brewing.

I believe Canal Park Brewing has one, it's called the No-Grainer. I haven't tried it, and I'm not certain if it's one of their standard offerings or a seasonal.

The question you would have to ask your doctor is: Does your wheat allergy extend to barley?

Since you don't have a gluten allergy, it is possible that you will not be allergic to barley. Considering the fact that most beer uses barley instead of wheat, you might be fine in most cases. 

While they are both grasses, they are of a different genus so you may not be allergic to both. The only person who can tell you for sure is your doctor.