Thanks for your question. Yes, this is completely normal for the first 6-12 weeks after any surgery around the orbit. There is a sensory nerve (2nd division of the trigeminal nerve) that exits a small opening on the front side of the bone where your surgeon worked to repair your fracture. This nerve gets bruised (extremely rare to be completely cut) during injury and surgery here. Light massage as tolerated is probably the best remedy here. Be sure to follow up w/ your surgeon next week. Best wishes.
What you are describing is related to the infraorbital nerve, which is immediately below the eye and supplies sensation for parts of the face you mentioned. This may be related to swelling in the area after the surgery. I would recommend that you follow up with your surgeon and discuss your concerns. Good luck!
Numbness tends to improve over months after the injury.
If it is compress related, perhaps it is best to stop.
Warm compress after surgery?
You should ask your surgeon about this. Not sure why you would use warm compress for an orbital floor fracture. Did you start with cold and then switch? It sounds like you are getting some swelling of the infraorbital nerve from the compress.