Okay, so the 'burning' sensation you're describing DEFINITELY sounds like an allergic reaction to SOMETHING. I'm not sure how long you've had these on, but could it be you have an allergy to latex and your mouth is still reacting from that? Or, it could be the nickel, as suggested. Either way, CALL THE ORTHO ASAP and they'll get you in. There is NO REASON for pain. Discomfort, yes; pain, NO!!!
As for what someone else said about not using the wax because you need to 'toughen up' your cheeks - this is wrong. Using the wax will ease the irritation from the bracket and help that area (or, in your case, those areaS) to heal, and just having that little bit of wax is enough to help your cheeks toughen up. Again, I will repeat - there is NEVER, EVER any reason to be in PAIN from braces.
Also, try rinsing with Colgate's Peroxyl or some other similar mouthwash that has peroxide in it. It will help your mouth heal much more quickly. The salt water rinse is also a great idea. Another thing I wanted to mention is something I've advised to others and still use (in fact, it's in my mouth now), and it's great -- Comfort Cover (
http://www.dentakit.com/cocoforbr.html or for ceramic brackets:
http://www.dentakit.com/brcoforcebr.html) This thing is fabulous because you put it across all your brackets at once and you don't have to worry about molding it (like the wax) or worry about it coming off, shifting, etc. Also, it's reusable...the only thing I wouldn't advise is eating with it in, as it gets full of the food. BUT, eating with wax in is not only FINE, it's ADVISED...since this is when so much movement is happening in your mouth that can cause friction between the brackets and your cheeks/lips/tongue. It is safe to swallow wax, so don't worry about that, either.
Another thing I would suggest is seriously limiting yourself to a soft foods (or even liquid)-only diet. There is a forum on here about soft foods...
viewtopic.php?t=20312.
Lastly, good luck and hang in there!!! And please, please, PLEASE give your ortho a call! If you NEED TO have the brackets taken off because of the pain, DO IT!! However, if there is any easing of the burning and/or pain, try to 'suffer' through it. And, I know you've said you've taken ibuprofen, but what about trying to get a prescription from your doctor for either a stronger dose of it or even one with codeine? And, have you tried taking, say 4 tablets/caplets?
Please keep us posted!! We're rooting for you.