It does look kind of serious--- probably a bacterial infection.. I suggest trying Copper spray on the bark(wear eye protection), alternated with Potassium Phosphite (such as Foliar Phosphite, K-Phite, Plant Doctor), each once a month, through early Spring.
If the oozing still occurs next Spring or Summer, give up on the friendly stuff, and use one or more conventional systemic fungicides / bactericides, and remove all fruit as they appear.