As of your history your child most probably have adenoid hypertrophic, adenoid is like tonsils situated posterior part of nose and due to enlargement of this gland block airway
That’s why your baby have snores.
If you want to know more about it
Search ashirwad hospital in YouTube there is one video on adenoid hypertrophy, I explain in detail about it in this video
Next Steps
Ask your Pediatrician or ent specialist for x- ray neck lateral side
Health Tips
There may be other causes too that may be rule out