I have braces and it becomes really difficult to play high notes. The highest I can play is a D on the top line. Any help on mouth position with braces?

I'm not sure 'mouth position' is going to be all that important. Remember that with or without braces the goal is to use only enough pressure to seal the air going from your body into your instrument. The embouchre I recommend is a soft, purse-string type embouchre. The more you 'smile' the sooner your lips will tire and the less of a range you will have.

With my students I use the same exercise for when they get braces on and when they get braces off. IT all has to do with training the lip muscle(s), and stretching or retracting the skin. And should only take a few days to show improvement.

My suggestion::
Each day you should play your horn. Here is a two-part 7 minute exercise that will help. If you can do this once in the morning and once before you go to bed at night that will be best. Start on 'C' just below the treble clef, play chromatically up to the 'C' third space, and then back down to the lower 'C'. Do this again going up to 'C#' and back down to 'C'. Again up to 'D'. Then 'D#', and then 'E'. What this is doing is retraining your orbicularis oris muscle and your depressor oris. This should take about 3 minutes. Don't rush and don't skip.

Part 2 - Start on 'G' (second line on treble clef) It is best to be looking at a clock with a second hand. Play the 'G' for 30 seconds (or as long as you can up to 30 seconds), rest for 15 seconds, and then play 'G#', again 30 seconds, rest 15 go to 'A', A#, etc up to 'G' above the staff. (This should take about 5 minutes)

Important:: (this is controversial but,) after playing the highest note. Do not play low notes to cool down or relax. Let you lips stay with the feeling of the highest note you played.

Try this: Roll your lips slightly inward so that less of the "red" is showing. Now place the mouthpiece to your lips in your usual way. This should help you to play higher, longer & stronger with less pressure and pain. Also, a grade school teacher I know says that tonguing on the lips instead of the back of the teeth helps reduce pain improves accuracy for her brass students with braces. These two effective techniques are taught in "The Balanced Embouchure."

Valerie Wells
"The Balanced EMbouchure" for French Horn
Wells123456@juno.com