Because Lantus is a depot insulin, Calley isn't getting the insulin you inject until a day or so later. The 176 isn't from the morning injection of insulin or possibly even last night's dose, but what was stored in her system before then. You'll be looking for evidence of the increase over the next several days.
I hope the vet is open to trying to address the nausea as a symptom of something separate from the diabetes. If not, I would personally be looking at trying another vet since this one frankly doesn't seem to be all that concerned with the symptoms Calley is showing.