I don't think I can expand on the title without diving into my personal symptoms which I believe are against the rules of this stack-exchange. Nevertheless, even a general answer should be helpful right now.
Please clarify your question, since paracetamol is not an antibiotic. Are you asking if the patient's symptoms are relieved by paracetamol and antibiotics, or do you mean if patient's symptoms are relived by paracetamol or antibioitcs? Thank you.
If a patient's symptoms are relieved by paracetamol it does not always mean their symptoms are caused by an infection. Paracetamol is an antipyretic and analgesic, it reduces a patient's fever and provides pain relief. However, not every source of fever and/or pain is caused by an infection. There are many non-infectious sources of fever. Most of them are immune-related diseases e.g. rheumatoid arthritis, lupus. Some are not, e.g. acute pancreatitis, cholecystitis, some neoplasias. But all are inflammatory (usually) .
As for antibiotics, if a patient's symptoms are relieved by antibiotics it is highly likely their symptoms were caused by an infectious disease. It's possible some antibiotics can be used to treat some non-infectious diseases. Personally I have never prescribed nor have I seen any medical professional prescribe antibiotics for this reason. But like many things, there are no absolutes.
I hope this answers your question, have a good day.