The greater tuberosity is a part of your upper arm bone near your shoulder outlined in green color below:
https://www.mdpi.com/applsci/applsci-10-06514/article_deploy/html/images/applsci-10-06514-g001.png
Most fractures in this region can be treated without surgery, as long as there are not too many displaced or angulated parts.
A greater tuberosity fracture without significant displacement normally takes 6-12 weeks to heal.
Signs of healing may include partial bony bridging and callus formation.
Please follow-up with an orthopedic surgeon for further workup and management.