Can I use the same syringe to inject two sites?

Hello,

This might be a stupid question, but I have just bought BPC157 to help address tendonitis in both knees. Is there any risk of Infection if I were to fill an insulin syringe, jab into one knee and inject half of the contents, remove the syringe, and immediately jab the remaining contents into the other knee? Of course the vial would be sterilised, and both knee injection sites would be sterilised using alcohol wipes.

Thanks!!