There are many allergy medicines for high blood pressure available in Texas.  Antihistamines are the most common allergy medication. Most of them seem to be safe if you suffer from high blood pressure, but always check with your doctor or pharmacist before you start taking any allergy medicine for allergies.  

Its not recommended to take  decongestants, unless your doctor tells you otherwise, because they may raise your blood pressure and also prevent some high blood pressure drugs from working effectively.  In addition, many allergy medications contain antihistamines and decongestants.  Hypertensive patients must avoid manufacturers’ combination drugs that add a decongestant element to regular formulas of antihistamine pills, sprays or liquids. These problematic drugs may contain phenylephrine, pseudoephedrine or oxymetazoline and may be labeled with a “D” after the brand name.

The Mayo Clinic lists prescription and nonprescription formulas such as desloratadine, fexofenadine and cetirizine that are both effective and safe for heart patients. Many offer once-a-day dosing, and some do not induce drowsiness side effects.

Sources:

webmed.com

Mayoclinic.org

livestrong.com