I would definitely call the allergist, and find out EXACTLY how long she has to have the antihistamines out of her system prior to testing. I'd also ask them, or a pharmacist, what else you can do for her in the meantime. The vinegar/honey mentioned could help with the coughing, you might also be able to try Deslym (it's nothing more than a cough suppressant, no antihistamines), but of course, check first to make sure it won't interfere with her upcoming tests.
I'd definitely also ask them to refill her nebulizer meds now... if she's having difficulty breathing due to asthma symptoms, which could most certainly flare up if she continues coughing and experiencing the level of allergy symptoms you describe, I wouldn't want to be without that, and I believe she can continue to use a nebulizer prior to allergy testing.
I wouldn't push her tests back just to give her antihistamines for the moment, because you would just be prolonging the agony, and she'll have to go through this eventually to have the testing done.
Best wishes. I know this is hard, we just did allergy tests for my son about 6 mos ago...
Blessings...