Can a person have a pulmonary embolism for a few months and only experience chest pain, is it possible ?

Possibly : Ct angiogram, d-dimer are tests necessary to assess for pulmonary embolism; a venous duplex (as a secondary test) may be required if you exhibit leg edema (swelling). Tachycardia is the most common manifestation of pe, not dyspnea or shortness of breath.

Small one: A small pulmonary embolism may only present with fleeting c/p and resolve with the body fibrinolytic sustem.