Pulmonary Embolism Support Group
By far the most common form of pulmonary embolism is a thromboembolism, which occurs when a blood clot, generally a venous thrombus, becomes dislodged from its site of formation and embolizes to the arterial blood supply of one of the lungs. Symptoms may include difficulty breathing, pain during breathing, and more rarely circulatory instability and death.

https://www.webmd.com/pain-management/costochondritis#1
I m not a huge fan of injections because 1. You will have to stop the blood thinner.
2. They create a havoc on your immune sustem, raise your blood pressure and blood sugar , affect your mood.
Before the injection, find out if they have holistic Physical therapist in your area.
One of the non-invasive methods holistic PTs use is electro-magnetic frequency.
You feel nothing during the treatment, by the device delivers waves in attempt to heal whatever is wrong by repolarizing the cell membranes.
There are clinical studies that show there is merit to this treatment .
I ve used it on a non-union of a fracture and it healed successfully in conjunction with other treatments.
Good luck and I hope you feel better
There are other things that can cause sternum pain like GI issues, pleurisy, hernia, etc. I would also make sure you are managing your stress.or any anxiety becaus I do think that can be part of the equation with pain sometimes.