Hello Jon,
Welcome to DoctorSpring. I have read your question with diligence and have seen your X-Ray. You have a fracture of the lateral end of clavicle. At present continue wearing the sling for support and the painkiller/ anti-inflammatory tablets.
You do need surgery. Ideally if you can have the surgery within the 1st week it is good. However even if you have the surgery around the 13th, it will not affect your recovery.
But surgery results are better when done within the first 24-48 hours or at the earliest. Cause with time there is abnormal tissue formation at the fracture site which effects the surgery slightly.
My advise would be , that if you can pre -pone your tickets and go earlier, it will be good. . However if it becomes difficult for you to go before the 13th DO NOT worry. Just make sure that when you reach, as the Osteopath said, do not waste time and get yourself treated immediately.
I hope this has helped. Feel free to follow up for any further queries.
Thankyou.