Honestly? I agree you are right to be dissatisfied with your present result. The under eye area is a very difficult area to inject, as another mumsnetter has already mentioned.
I have had filler in my cheeks (and the last couple of years my marionette lines) for 9 years now, and I have always had a good result. This is because my practitioner understands facial structure, where and how to place filler and how to avoid mistakes and injury. She goes on courses to update her skills regularly. She is actually a Dentist who trained to administer dermal fillers and Botox too over a decade ago now. She has both clinics at her practice, dental and facial.
She told me that she is shocked by some of the questions people ask on training courses and that they shouldn’t be allowed to practice. She had a nurse who assisted her (not injecting, administering numbing cream, passing syringes etc) who left to set up on her own, injecting fillers and Botox and she did not agree with it at all.
So I think you should go back to them and claim a refund. I don’t know where you live or I would recommend my practitioner as she likely could put it right for you. A skilled practitioner could do that. I am sorry that your result is not good, and I am sorry for it.
But it can take up to a month for filler to settle, so it may improve in the next two weeks. But if it does not, I would not let the same person inject your face again.
I hope I haven’t upset you by anything I have said in my reply, but you asked for honesty and I have 100% given it.