It is possible. In WA, not having a BAC is often very helpful in minor consuming alcohol cases.
I am not an insurance rep and make no recommendation on any company.
If there is other evidence you were drinking (i.e., a witness, you were holding a can of beer, odor of alcohol, slurred speech, etc.), the fact there is no breath test will not matter. All the prosecutor has to prove is you were underage and you were drinking alcohol. And the burden of proof is not the highest standard you are used to hearing about in criminal cases - beyond a reasonable doubt. The burden for your case is clear and convincing evidence, something less.
And if the reason you could not do the breath test is you were "too drunk" as you claim here, then there is likely ample evidence you were drinking alcohol.
Some jurisdictions will offer to dismiss or amend an underage drinking, even a 2nd in 1 year, if you complete an alcohol education course. You may at least be able to avoid a driver license suspension.
For more specific advice, contact a local, experienced criminal defense attorney. Criminal defense attorneys generally handle these types of cases, as well.
Karen Missmer is right. There is a defense if you were consuming alcohol with your parents. It is not against the law to have alcohol in your system even if you are underage, if the alcohol was legally consumed, under the supervision of a parent or guardian. The fact that a parent or guardian was not with you when the arrest was made does not matter so long as you didn't consume other alcohol outside their presence.
Sign up to receive a 3-part series of useful information and legal advice about DUIs.