It would depend on many factors. Have you first tried calling the dental office that you have an apt for, to see if they can not get you in sooner?
Since you are looking for a referral for orthodontic I am guessing you have some insurance in place. Or you would not need a referral just to go to the orthodontic. Since this is the case call your insurance carrier and see if they can advise you a different general dentist you can go to for the referral.
For the most part a dentist office would not see a referral to an orthodontic as an emergency. But you may be able to find a dentist you can go to that is not so far booked out.