Will oral gonorrhoea go away on its own?

Unlikely: This can be a serious infection which can break though the barriers of the mouth lining and cause serious damage in the rest of the body. Do not rely on spontaneous healing; the risk is too high. I am guessing that you don't want the embarasment of discussing this with anyone but in this case a little embarrasment is worth the treatment.

No: Gonorrhoea is treatable with antibiotics and doesnt go away on its own. http://patient.info/doctor/gonorrhoea-pro