Getting fevers intermittently for last one month did a course of amoxicillin & mextra. for few days everything remains fine then suddenly start fever?

FUO: You have a fever of undetermined origin. This is the topic of numerous articles, chapters and books. Most are non-infectious, but for those that respond, as yours, to antibiotics, one must be concerned about a heart valve infection, a hidden abscess, and so on. You should see an Infectious Diseases specialist ASAP. Do not neglect this. Hopefully this will be benign but has potential to be fatal.