Meloxicam and Aleve (naproxen) belong to the same class of drugs called non-steroidal anti-inflammatory drugs (abbreviated to NSAIDs) and are used to relieve pain and fever and reduce inflammation. They are used to treat mild-to-moderate pain caused by conditions such as headaches, menstruation, migraines, arthritis, sprains and strains, and toothache.
NSAIDs can be used in combination with Tylenol (acetaminophen) for moderate pain not relieved by NSAIDs alone.
It is best not to take more than one NSAID at the same time as you increase your risk of experiencing side effects.
Side effects most commonly include gastrointestinal upset such as bloating, diarrhea, constipation, irritation of the lining of the stomach, nausea or vomiting. NSAIDs also affect kidney function and reduce how quickly blood flows through the kidneys. They may cause retention of sodium and water which can lead to edema and high potassium levels. Some NSAIDs have a high risk of cardiovascular thrombotic events such as a heart attack or stroke. Asthma, headache, insomnia and hives are also side effects of NSAIDs.
It would be safer for you to add Tylenol to either meloxicam or Aleve but you should not take meloxicam and Aleve together.
If the pain does not go away or gets worse see your doctor.