How can I heal ice burn under eyes after Botox?

Botox is great for the crow's feet and an ice roller is not necessary afterwards.  I would call the treating physician and ask them what they suggest.  In the meanwhile I would treat it topically with a soothing cream or aloe vera gel.

You an apply a topical hydrocortisone to help calm the redness, after a bit of cool water. It should resolve within a day or so depending on how bad the burn was. Sorry this happened!"This answer has been solicited without seeing this patient and
cannot be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."