While an older breathalyzer might have confused ketones with alcohol, the human nose is actually more discerning. Any capable doctor smelling Caroline's breath would have immediately recognized it as ketones rather than alcohol.
When the doctor administers insulin to Caroline, he says he's giving it subcutaneously but rather injects in the arm which would be intramuscular. Moreover such a large quantity such as 10 millilitres is never injected in the arm.
28+ minutes into the show when Caroline is stopped just before she is breathalyzed by the police, Caroline opens her car door and the production crew can be seen in the reflection of the door as it opens.