Question about health care enrollment

I'm about to hit my one year next month and was sent packets containing all the health care plans and whatnot. I received it two weeks ago and figured I would have some time to fill it out. I asked my bud at work if he had sent his out already and he said that I should've already done it cuz there's a deadline. Sure enough, I read it today and it said the last day for them to receive it was the 24th. I immediately filled it out and faxed it to the number they provided. I'm worried that I'll get screwed and they won't enroll me
 
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