You can apply for private loans at any time. They are generally sent along with your regular loan disbursement unless you apply off-cycle with your federal aid, in which case the first disbursement is sent immediately.
I use THE (northstar) and highly, highly recommend them.
I get a real person on the phone every time, they have no fees and they will take the time to explain things and answer any questions you have.
I have had 4 total lenders through college and medical school and I only wish I found them sooner. I wont use anyone else.