First things first: Always check with your doctor or pharmacist before you start to take any medication -- for allergies, high blood pressure (also called hypertension), or anything else. That's true for herbs and supplements, too.
Antihistamines are the most common medication for allergies. Most of them seem to be safe if you have high blood pressure -- but again, ask to make sure.
Don't take decongestants unless your doctor tells you otherwise. They may raise your blood pressure. They also keep some high blood pressure drugs from working the way they should.Be careful, because many allergy medications contain antihistamines and a decongestant.
Watch out for combination medications for allergies that include decongestant ingredients. That includes allergy drugs as well as many remedies for cold, flu, and sinus problems. Ask your pharmacist to check the ingredients for you.