My experience as a woodwind teacher of many years is that braces affect people differently. Some of my students have had to give up until they come off and others have sailed on to Grade 8 with Distinction! Depends what they do to you really.......
However, what I would say is a common thing is that braces hurt when they are first put on (and when they are adjusted) and they do affect your embouchure. As the shape of your mouth changes as the teeth move, you will need to continue to adjust too. Your teacher will help you with this, I'm sure. I'd also say to ask him/her what he/she thinks about the timing of the fitting of your brace.
For myself I would say wait until the exam is over. You may find it difficult to get the upper register initially after the brace is fitted and you don't want to be stressing out in the exam if you're not on top of the technical aspects of your playing. I cannot believe delaying two months will seriously affect your teeth but you'd need proper advice on that. If you've already had some teeth out to prepare for the brace then there may be greater importance in the timescales.
Finally, remember an examiner can only examine what he/she hears. They cannot "second guess" how you would have played without your brace or start making allowances for it. If you are not ready for your exam my advice would be (as it is to my own students) don't take it. Wait until you are comfortable and ready.
Best of luck whatever with the braces and the exam!
