Are there any prescription antihistamines?

A few. Antihistamines have been around for many years & many that used to be prescription are now available over-the-counter. A few antihistamines are still prescription, including some first-generation (sedating) medicines like periactin or palgic as well as second-generation (less-sedating) medicines like xyzal (levocetirizine) and clarinex.
Yes. There are both sedating and non-sedating antihistamines that require a prescription. Some insurance companies will not pay for the prescription drugs Clarinex or xyzal, (levocetirizine) which are the slightly changed versions of Claritin and zyrtec, unless your physician requests "prior authorization".