Hired, but no start date yet? Should I be worried?

[Sydrose]

Last month (may) I went for 2 interviews for the same position (CNA) and was later called and offered the position and I of course said yes. I did my physical, drug test, and new hire paperwork. I waited for an email of what to do next, because i knew I would not be able to do orientation until July. Well, time continues to pass and still nothing. I emailed the lady who hired me and she has still not answered. So I called and she told me I needed to bring my id and papers to finish the paperwork. I brought them to the interview last time but she didn't even ask for them. I just feel like somethings gonna go wrong and I won't end up with the job. Should I be worried? I put my notice in already at my current job and I'm freaking out!