You point to very important question.
Reactie arthritis. What is reactive arthritis? Most of the rheumatologist put diagnosis of reactive arthritis (ReA) when 5 condition are present.
1. 100% proven presence of current infection that has naver been present before, so to consider unambiguous that this infection is the only and sure causative for the reactive arthritis. Of course there are different types of bacteria that are listed to cause reactive arthritis, but this list is a floating list, and not strict. But keep in mind that there is evidence that viruses may also cause reactive arthritis, so the antibiotic 'thing' (which acts only on bacteria), is realy not important here.
2. Presence of symptoms and pathology that fits in the seronegative spondiloarthropaties group (reactive arthritis is a part of the seronegative spondiloarthropaties group). Mostly tendons and ligaments affected, very mild if any synovitis, and migratory pattern.
3. Strongly negative rheumatic diseases antibodies tests (-ANA,-RF...and etc) (reactive arthritis is a part of the seronegative spondiloarthropaties group, that mean these test are negative) (Otherwise they should put dx RA, or SLE..or etc.)
4. Absense of psoriasis and inflamatory bowel disease (otherwise thay should put dx psoriatic arthritis (PsA) or arthritis associated with IBD).
5. Mild spine and sacroliac joints envolvement (otherwise they should put directly dx: Ankylosing Spondilitis - AS, which is actually a type of reactive arthritis to a gut bacteria)
When 2,3, 4 and 5 are only present (without 1) some docs says that it is reactive arthritis with unknown causative infection, but most of the doctors puts temporary diagnosis of undiferentiated arthritis (so they just have no idea what's wrong with you, but ashame to tell you) and puts you on NSAIDs, may be on wide spectrum abx for week or two, and then starts to 'wait for development'. Actually they do the same if they found you have reactive arthritis too. Abx are tought to do their job for 2 may be 3 weeks not longer. And actually this statement has much accuracy in it because as much abx you take the most resistent the bactaria becomes, and that's how the chronic infections heppens. Bacteria of any types are present in the human body and they live in symbiosis with us. All these types of bacteria is IMPOSSIBLE to be eradicated, so we are talking only about balance, the bacteria usually live in our GI tract (mouth, guts) and genitals, eyes. Our saliva, mucus, tears and our antibodies and pH found on these surfaces doesn't allow the bacteria to grow enough to cause us infection symptoms (so we live as healty). And when some bacteria somehow succeed to grow enough to cause infection (like in your case the sinus infection), then local symptoms on the affected tissue usually appears. Ex. cough is a symptom of bacterial pneumonia (not only)...and etc. Then the abx comes to help. It does not eradicate bacteria but inhibits it's multiplication in order the immune system can cope with the crisis situation. The prolonged use of antibiotics first: disturbes the natural balance bacause it takes the work of the body itself to manage it, and second makes tha bacteria more resistent, but does not eradicate it comletely. It is not recommended to take abx for very long period unless it is proven effective, thats why some doctors, knowing these facts, refuse to treat patients with abx for chronic infections, but exactly the opposite, they try to manage the infection naturaly, to recover the natural balance (I'm talking about non immune-suppressed people, people not taking immune supressing medications) And finally...: if the ReA is caused by a virus, abx does not act on the viruses, and smth more they act weakening on the immune system, and immune system is the only unit that can cope with a virus infection, so.o.o you must take care for it to be strong as possible. So the things are not such simple: got bacteria, take abx untill the bacteria die, and you become sterilized and healty again, because you will never become sterilized, as long as there is life on earth.