Please help! What is the terminology for a person who is nearsighted in one eye and farsighted in the other?

Anesometropia. That is the definition. Myopia is being nearsighted and hyperopia is being farsighted. While presbyopia is when you are unable to accommodate and focus up close, usually begins over the age of 40.
No specific term. As already mentioned, anisometropia applies here and means that there is a different refractive error in each eye. There is no specific term form farsighted in on, nearsighted in the other eye. One exception, if you are purposely corrected for a little nearsighted in one eye, and for distance in the other, that is called "monovision" and aims to avoid reading glasses. Hope this helps!
Antimetropia. When one eye is nearsighted and the other is farsighted the term that describes this is antimetropia.