I have three wind instrument players who had braces put on and my oboist had the toughest go with it when they were first put on and during adjustments. She also had a device placed in the roof of her mouth that required tightening every other day. She has stated that it was when the braces were first put on and then at subsequent adjustments (every 6-8 weeks) that she found the most difficult and painful to maintain correct embouchure while playing. When first put on, all three of my daughters agree that the average time seemed to be 1-2 weeks where there was soreness in general and that was the worst, but adjustments - especially in the beginning also caused pain. After speaking with her Orthodontist, he suggested that she take 2 Tylenol or Ibuprofin profylactically about 1 hour prior to her lessons. This seemed to at the very least help, but sometimes provide enough relief that she was able to work back up to hour lessons. He also suggested, that just for a while, practice sessions during the week be broken into shorter sessions - about 15-20 minutes at a time, but that she could start with one practice period a day and then when she felt she could add another she could and then another & so on. Ibuprofin has anti-inflammatory properties and I found that was a better choice for us. (Also a bit better on their young livers.) So what worked well for us was the 2 over-the -counter pain relievers and a LOT of wax.
As for the guards/shields, our orthodontist felt that the additional bulk made the process more difficult. (He has a daughter who played the clarinet when her braces were put on) but each Orthodontist may have have their own opinion regarding this.
If there are ANY areas that the student feels a brace or wire "poking" the cheeks, gums or tongue, orthodontic wax should immediately be applied and can be on the area during playing. It does take time to get used to getting the wax on correctly - it should be put on the brace or tooth dry and using an ample amount helps. We'd take napkins or paper towels to dry the area before applying the wax. Lastly, there is a product in lieu of the wax that was given to us by our Orthodontist which, if I recall, was called cement wax and was much stronger and stayed in place better. It made me wonder why he hadn't given us that in the first place! It is similar to the wax, but just thicker and comes in a double-tubed push applicator which made it easier to reach places in the back that we're aggravating her mouth. If you'd like me to, I can find one if these tubes to give you the exact name & brand. We got it from the Orthodontists and I've never seen it at a drug store. Just let me know and I'll look for it. I know we still have a tube or two around somewhere.
Being in the medical field, I must say that even over-the-counter medications should not be given or even suggested without having the parent check with the primary care physician or pediatrician of the student who is familiar with their entire medical history.
I hope that helps. I will mention that when the braces come off, there is again a period of adjustment, but at least it isn't painful and seems to be brief.
Best of luck,