Why do you think you should be reimbursed since you developed a complication? Did you think the procedure did not carry any risk, that complications were not possible? Let's say you had your appendix removed, developed some scar tissue which caused you some pain, do you think you should be reimbursed? I can tell you that the complications from any procedure (other than cosmetic) would not be treated for free, so consider the additional service your doctor is providing for you. It does not seem that your doc is at any fault in causing your symptoms, only then would you be entitled to a refund. To rule this out you need to ask your doc what exactly was in the new hyaluronic acid, any preservatives or other chemicals?
If you think medical procedures carry no risk you should not be getting elective procedures.
As to what's going on with your lips. Could be infection from bad lipsticks/makeup. Could be herpes, could be lots of things.