Will sodium naproxen coupled with extra strength tylenol affect blood tests that look for inflammation and autoimmune disease the day after taking them?

Not likely: These medications are not likely to affect the auto-antibody titers nor the CRP levels. By taking both medications, you are overdoing pain medications. Have a healthy diet, exercise 30 minutes/day, drink plenty of water, have safe sex, no tobacco alcohol weed or street drugs. For nutrition: http://www.choosemyplate.gov/. Wish you good health!