Recurrent fevers and chills

My daughter had been having fevers and chills almost daily for almost 3 months. A few weeks ago,  she started having swollen legs and ankles and feet. Her joints are not hurting, Rather, the muscles are painful to the touch. Many esoteric blood tests had been done to rule out infections, auto immune diseases, rheumatoid arthritis and even sarcoidosis. All came back negative or normal except for some non specific inflammatory tests such as ESR, CRP, WBC which are highly elevated. Two specific tests for possible rheumatic fever, ASO and ADB are high borderline the normal range. She had been seen by a rheumatologists who was also looking to rule lymphoma and/or leukemia. Her weight is stable and her appetite is great. When she experience the fever and chills episode, she's tired and need to take a nap. The whole thing could pass in a couple of hours and then she would be able to eat, do home work and go to school again the next day. The chill and fever normally come on in the afternoon, evening. If she has a fever at night, she would sweat profusely during the night. The longest period she had gone without fevers and chills is about 3 days without swelling of the legs. The doctor put her on Naproxen, 375 mg twice a day. It doesn't seem to work. We might try 500 mg. I would like to know if anybody has any theory on this.