If you sue, you have the burden of proving, by a preponderance of the evidence, that the health care provider breached its duty of ordinary care, proximately causing damages to you. Maybe a jury would give you a dollar.
[In accordance with the community guidelines of Avvo, this is not "legal advice", nor does it form an attorney-client relationship.]
The question you need to have answered is whether in your jurisdiction this constitutes malpractice or negligence which is actionable, In addition, although clearly stressful adn without intending to minimize what you went through, the key word you wrote is "almost" That sounds like you are saying you "almost" were injured, and in order to bring a suit you must have been injured. You should clearly consult a local attorney in your area who handles these types of cases
The response herein is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question.