Eye crossing IN towards the
noseNose fracture is called esotropia. Most children whose eyes cross before 6 months of age have large obvious eye crossing that needs treatment with surgery (and sometimes also glasses and patching). Whether or not he switches between eyes when crossing is not relevant to needing surgery. The question with surgery is whether or not he keeps his eyes straight more than 75% of the time. If yes, then surgery is not urgently needed. If no, and glasses are predicted not to be helpful, then surgery is needed.
It sounds as though your son's actual glasses prescription might be fairly mild which is why there is some doubt about the usefulness of glasses as part of his total treatment.
You should visit the Parent Question forum at www.aapos.org and research Esotropia, Congenital Esotropia, and Accommodative Esotropia.