Am I able to join the Army or Air Force if I was hospitalized with ethanol poisoning recently?

Went to a bachelor party a couple of months ago and the liquor delayed and caught all up on me at once and I got way too drunk and spent a night in the hospital for alcohol poisoning. I talked with an Army recruiter last year and took the asvab. I want to join as a 35F or join the Air Force but I am worried that I will not be able to join (especially in a job that requires clearance) for an extended period of time because of the hospitalization and that I would not qualify for service in the military. Is this an accurate fear? Thanks for any answers.