I want to ask a question about which doctor to go see given that my family doctor is now clueless about it (second and third advices are also clueless). Is it on topic?
No, I don't think it is on topic. If you're asking for guidance about a particular physician or group, in addition to being a personal advice question, it's essentially a recommendation request and therefore likely to be opinion-based and a poor fit for the SE format.
On the other hand, if, by "which doctor" you mean which type of doctor (i.e. which sub-specialty), this might be more of a healthcare systems question that could be on topic. It would need to be carefully phrased to avoid being "opinion-based". It's possible to demonstrate objectively that a particular subspecialty routinely deals with a particular condition or set of symptoms, for instance, and this may be informative for your question.