Infectious or allergic cough in a child with a disability due to neurology

Hello, help, please advice. Daughter is 5 years old, does not speak (we have a disability due to neurology), a cough began to appear a couple of weeks ago. I started with a dry one, I began to use expectorants (Linkas, calamus root), it changed to a wet one. Strong anxiety does not deliver the child. Appears mainly in the mornings and evenings, in the afternoon less often. No temperature, no rhinitis. General condition is not changed. Allergies have never been on anything, rarely get sick. Tell me what to do to understand what kind of cough is allergic or is it a sluggish infection? Can I give my child an allergy medication and see if the cough disappears?