Hi, I understand that your main concern is whether you have Rheumatic fever or not. There are certain criteria that have to be met to diagnose Rheumatic fever (not just repeated elevation of ADNase titre), which include few major criteria like Carditis, Polyarthritis, Subcutaneous nodules etc and minor criteria like fever, joint pains, ECG changes etc. Confirmation of diagnosis can be done when two major or one major and two minor criteria are present. Moreover, there has to be evidence of recent streptococcal infection. Regarding your kids symptoms like bleeding nose, abdominal pain etc I suggest that you take them to a Pediatrician in order to make a correct diagnosis by doing a physical examination. And regarding use of antibiotics, first a firm diagnosis has to be established to know whether a single dose of antibiotics would fix this or there is need for prophylaxis. Take Care!