For what it is worth here is my 'fivepenn'th'.
Follow your dream! Go back to the orthodontist and ask to have the permanent braces removed and replaced by a brace that can be worn at night while asleep and taken off during the day.
My son, who had the same dream as you, had to wear the sort of brace I have described during his mid-teen years.
He said he wanted to be a Jaguar pilot when he was 8 years old, applied to the RAF when he was 16 and was awarded a Sixth form scholarship. Joined at 18, and started on the Jag' OCU when he was 21.
My advice is to forget university if you have a genuine chance of being offered RAF pilot training. You will have lots of hurdles to jump and if 2 or 3 years down the line you haven't succeeded, university will still be there - my feeling is doing it the other way round may not bring the desired result.
Incidentally, even if you end up with better teeth after your treatment is over, you could still lose them playing sports such as rugby or cricket
.
Good luck - I hope you fulfil your dream!