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All anti-inflammatory drugs such as ibuprofen (Advil, Motrin), naproxen (Aleve),celecoxib (Celebrex), meloxicam (Mobic), etc. can increase blood pressure. One may increase it more than others in any given person. Trial and error is the only way to determine that.
The mechanism is a convoluted one involving the NSAIDs (non-steroidal anti-inflammatories like Advil and Aleve) effect on prostaglandins in the kidneys that ultimately lead to an increase in blood pressure.
Blood pressure can be taken at any time of day. Any kind of stress (such as having to urinate or have a bowel movement) may increase it. So will pain, such as a headache, or worry or anxiety, caffeine, smoking, etc. Blood pressure varies throughout the day usually being higher in the afternoon than in the morning. It also varies up and down depending on whether someone has eaten, had something to drink, smoked, talked, had exercise, etc.
To take a good blood pressure reading, wait until 30 minutes after eating, drinking, smoking, etc. Sit quietly in an upright chair with back supported and both feet on the floor for 10 minutes. Don't cross your legs even at the ankle. Both feet should remain flat on the floor. Apply the blood pressure cuff as directed. Support your arm at heart height on a table and engage the blood pressure device - either use the bulb and a stethoscope (difficult to do on yourself) or an electronic monitor.
Choosing the same time each day to record your blood pressure may be most useful if you are keeping a log for your cardiologist.
Please let me know if you have questions.