The patient's grogginess, dry mouth, and difficulty voiding are likely due to:

The symptoms of grogginess, dry mouth, and difficulty voiding are indicative of the anticholinergic effect commonly associated with certain over-the-counter medications. Anticholinergic drugs block the action of acetylcholine, a neurotransmitter involved in many bodily functions, including the regulation of salivation and urinary function. When these medications are taken, they can lead to a decrease in saliva production, resulting in a dry mouth, as well as disrupt normal bladder function, causing difficulty in urination. This mechanism can also cause sedation or grogginess, contributing to the overall symptom picture presented.

The other potential causes, while relevant in some contexts, do not align as closely with all three symptoms. Allergic rhinitis typically presents with nasal symptoms and is less likely to cause grogginess and urinary difficulties directly. Drug-drug interactions could lead to similar symptoms but would require a specific context or combination of medications to produce the anticholinergic effects. Acute prostatitis can affect urinary function, but it would not commonly cause grogginess or dry mouth as primary symptoms. Thus, the anticholinergic effect of over-the-counter medications best explains the combination of symptoms in this scenario.