Congratulations!
Oboe/flute with braces is fine. I play the oboe with braces, and my teacher usud to.
taking out teeth does hurt for a couple of days and getting braces fixed isn't nice the first few days and after tightening, but apart from that, after you got used to them, it's no big deal at all.
it'll be easier to get a good embouchure on the oboe after the braces are off
Braces do cause cuts/ulcers inside the mouth especially when playing the oboe as well, so ask the orthodontist for wax (i think it's called that. it's a waxy thing that makes the part that's causing the cut smoother so it doesn't hurt as much.)