While you are wearing your braces the most important thing to remember is to NOT injure your lips. Cuts, tears, bruises ect can lead to scar tissue. Scar tissue is permanent and depending on how severe it is could completely stop you from playing. A less severe case will lead to a bad sound and poor lip slurring ability.
There are several ways to hurt your lips while wearing braces.
The braces ARE going to PIN the lips in place. In other words they will be locked into position the second that the mouthpiece makes contact with your lips. Moving the mouthpiece around while playing WILL injure your lips. Some players do lots of adjustments after the mouthpiece touches the lips. This is a NO-NO.
You need to make sure that the lips are set for the upper register always. You can relax them to play low but you can NOT make them close the aperture while they are locked in place. Set your lips for a g on top of the staff. From this point high c is a half an octave away and low c is 1 and 1/2 octaves away. (Younger players would set lower ie a 4th space e, or for Elem students a middle c . Due to having less range.) This means that you don’t need to adjust your chops as much when you play. This can save you while you are wearing braces.
Second you need to back off the mouthpiece to lip pressure as much as possible. With a close aperture setting and always setting for g on the staff you need very little pressure to complete the seal. You will no longer have any need to use the octave key (little finger hook) to aid in making the lips closer together.
Third avoid Shakes, hand vibrato and large pivot movements.
Fourth work on skills that will carry over after the braces come off. Things like tonguing skills, improv skills, lip slurs. In other words don’t jump out there and play lead in the jazz band. Even if you can play that high there is TOO great a risk for injury.
Lastly I want to say that Wayne had a great suggestion about the teflon tape found in the plumbing section of hardware stores. I can see how a strip of that tape folded in half could be a very good barrier for some players with braces. That could even help some players who don’t have braces but do have a sharp tooth edge that sometimes cuts the lip.