Typically no. Antihistamines are generally not considered a group of medications that directly cause gout. However, antihistamines can cause dryness, and if that progresses to dehydration, then gout attacks can occur with a higher frequency. This would be an indirect cause. Antihistamines generally don't cause significant dehydration. Aspirin can make gout worse, as can other salicylate-containing meds.
No. Antihistamines do not cause gout.