Hello Marjorie, Thank you for trusting HealthcareMagic Nosebleeds can be due to several reasons like dry climate, trauma, medications like aspirin and warfarin, hypertension, bleeding disorder etc. Systane eye drops do not cause nosebleeds. Since you have a history of hypertension along with nosebleeds, it is important to check if blood pressure is well controlled.If blood pressure is not well controlled, you might need an increase in dose of antihypertensive medication/ change of medication. If you are experiencing dry nose, using saline nasal drops and humidifier in your room can help relieve recurrent nose bleeds. Effective control of blood pressure is also very important in preventing nose bleeds. While having active bleeding from nose sit upright ,lean forward and pinch your nose with your fingers for at least five minutes which will control the bleeding. After that apply ice pack on nose. Avoid using nasal drops containing oxymetazoline/xylometazoline since you have hypertension. Effective treatment and prevention of nose bleeds require identification of underlying condition. Please follow u with a primary care provider for further evaluation. Hope I was able to help you Please address any more concerns Regards, Dr.Lekshmi